jkffi 2003

International Conference on

DIFFERENTIRL EOUfiTIONSHasselt, Belgium 22 - 26 July 2003

Edited by

Freddy DumortierLimburg University Centre, Belgium

Henk BroerUniversity of Groningen, The Netherlands

> Jean Ma whini Catholic University of Louvain, Belgium

Andre VanderbauwhedeUniversity of Ghent, Belgium

Sjoerd Verduyn LunelUniversity of Leiden, The Netherlands

World Scientific! N E W J E R S E Y • L O N D O N • S I N G A P O R E • B E I J I N G • S H A N G H A I • H O N G K O N G • T A I P E I • C H E N N A Ii

CONTENTS

Preface v

Plenary lectures 1

E. Castella and A. Jorba, The Lagrangian points of the realEarth-Moon system 3M. Golubitsky and I. Stewart, Synchrony versus symmetry in coupledcells 13M.D. Groves, Three-dimensional solitary gravity-capillary water waves 25V. Yu. Kaloshin, Mather theory, weak KAM theory, and viscositysolutions of Hamilton-Jacobi PDE's 39P. Krejcf, An application of non-smooth mechanics in real analysis 49R.S. MacKay, Chaos in three physical systems 59J. Mallet-Paret and S.M. Verduyn Lunel, Mixed-type functionaldifferential equations, holomorphic factorization, and applications . 73R. Ortega, Competitive systems with three species and periodiccoefficients 90P. Polacik, Asymptotic symmetry of positive solutions of parabolicequations 99R. Roussarie, Bifurcations of Planar vector field unfoldings . . . 109K. Schmitt, Positivity, continuation and nonlinear eigenvalue problems 119F. Takens, Time series analysis: smoothed correlation integrals,autocovariances, and power spectra 128Y. Li and Y. Yi, On Poincare - Treshchev tori in Hamiltoniansystems 136

Mini-symposia 153

Computational aspects of differential equations andapplications (Org.: B. Krauskopf and K. Lust) 155

S. Day, O. Junge and K. Mischaikow, Towards automated chaosverification 157

E. J. Doedel, D. J. Dichmann, J. Galan-Vioque, H. B. Keller,R. C. Paffenroth and A. Vanderbauwhede, Elemental periodic orbitsof t h e C R 3 B P : A brief s e l e c t i o n of c o m p u t a t i o n a l r e s u l t s . . . . 1 6 3D.J. Estep, S.M. Verduyn Lunel and R.D. Williams, The formationof shear layers in a fluid with temperature-dependent viscosity . . 169K. Green, K. Engelborghs and B. Krauskopf, From local to globalone-dimensional unstable manifolds in delay differential equations 175A. Jorba and E. Olmedo, A parallel method to computequasi-periodic solutions 181K. Lust and K. Verheyden, A Newton-Picard collocation methodfor computing periodic solutions of delay differential equations . . 184H. Osinga and R. Rokni, Numerical study of manifold computations 190B. van de Rotten and S.M. Verduyn Lunel, A limited memoryBroyden method to solve high-dimensional systems ofnonlinear equations 196G. Samaey and D. Roose, Computing connecting orbits indelay differential equations using DDE-BIFTOOL 202

Water waves (Org.: M. Groves and M. Haragus) 205

A. Constantin, Wave-current interactions 207G. Schneider and O. Zink, Justification of the equations for theresonant four wave interaction 213B. Schweizer, Viscous water waves in a bifurcation approach andconnections to inviscid theories 219

Topological and variational methods (Org.: J. Mawhin) 225

J.A. Cid and R. L. Pouso, Existence results for discontinuousordinary differential equations 227D. Bonheure, Multitransition connections for fourth order equationswith a bistable nonlinearity 230D. Bonheure and J.M.Gomes and L.Sanchez, Positive solutions of asecond order singular ordinary differential equation 234A. Canada and D. Ruiz, Resonant systems with periodic nonlinearity 237Y.A Klokov and F. Sadyrbaev, Sharp conditions for the superlinearityof the second order ordinary differential equations 243A. Krasnosel'skii and D. Rachinskii, On the number of branchesof periodic solutions 246

|?.M. Minhos and A.I. Santos, Existence and non-existence resultsfar two-point boundary value problems of higher order 249Jj; Rachunkova and M. Tvrdy, Method of lower and upper functionstn impulsive periodic boundary value problems 252A.M. Robles-Perez, Almost periodic solutions of forced sine-Gordonequations 258R. Srzednicki, Isolated sets of solutions of two-point boundary valueproblems and their indexes 264D. Ruiz, A priori estimates and existence of solutions for nonlinearproblems involving the p-Laplacian 270

Qualitative theory of nonlinear parabolic andelliptic equations (Org.: H. Matano and M. Fila) 275

J.M. Arrieta and A. Rodriguez-Bernal, III posed problems withsupercritical nonlinearities 277J. Eisner, M. Kucera and L. Recke, Smooth bifurcation and variationof the contact sets for an obstacle problem 281M. Fila, H. Matano and P. Polacik, Immediate regularization afterblow-up 284G.V. Grishina, Asymptotic behaviour of solutions to semilinearelliptic equations in unbounded domains 290J.M. Arrieta, A. Jimenez-Casas and A. Rodriguez-Bernal, Fluxcondition induced by concentrated reactions 293R. Ikota and E. Yanagida, Stability analysis for the curvature-drivenmotion of curves with triple junctions 296B. Kawohl, Symmetry in anisoptropic media 301M. Kucera, J. Eisner and L. Recke, Smooth bifurcation andexchange of stability for variational inequalities 307R. Stariczy, On some elliptic equation with nonlocal nonlinearity . 310M. Winkler, Nonuniqueness in strongly degenerate diffusionequations with strong absorption 313

Around Hilbert's 16th problem (Org.: Y. Ilyashenko,R. Roussarie and F. Dumortier) 317

M. Caubergh and F. Dumortier, The use of Melnikov functions inmulti-dimensional parameter families: algebraic curves ofmaximal cyclicity 319

J. Chavarriga, H. Giacomini and M. Grau, Quadratic systems withan algebraic limit cycle of degree 2 or 4 do not have a Liouvillianfirst integral 325B. Coll, A. Gasull and R. Prohens, On a criterium ofglobal attraction for ordinary differential equations 328LA. Garcia, J. Gine and H. Giacomini, Generalized nonlinearsuperposition principles 334LA. Garcia and D.S. Shafer, Limit sets of planar vector fieldsand the vanishing set of inverse integrating factors 337A. Gasull and J. Torregrosa, Some results on rigid systems . . . 340Yu. Ilyashenko, Persistence theorems for holomorphic foliationsand Kupka-Smale property for polynomial automorphisms of C2 . 346M. Sabatini, Coexistence of centers and limit cycles inLienard systems 354H. Zhu, From the PP-graphics to the finiteness part ofHilbert's 16th problem for quadratic systems 357

Navier-Stokes equations and reaction diffusion equations(Org.: R. Farwig and M. Wiegner) 363

H. Abels, Reduced Stokes equations and bounded Hoo-calculus . . 365R. Farwig, Flow around rotating obstacles - analysis of a singularintegral operator 371P. Kaplicky, Some remarks to regularity of flow of generalizedNewtonian fluid 377J. Malek, G. Mingione and J. Stara, Fluids with pressure dependentviscosity: partial regularity of steady flows 380V. Roussier, Long-time asymptotics of Navier-Stokes andvorticity equations in a three-dimensional layer 386A. Raczyriski, A singular problem with non-constanttemperature - steady states 389J. Saal, The Stokes operator with Robin boundary conditions

in L2°(K") 392O. Sawada, On analytic properties for the strong solutions to theNavier-Stokes flows 398B. Schweizer, A priori estimates for the Euler equation witha free boundary 401

Hyperbolic dynamics and beyond (Org.: M. Vianaand V. Araujo) 407

J.F. Alves, K. Oliveira and A. Tahzibi, On the continuity ofentropy for non-uniformly expanding maps 409Ifv. Araujo, Integrability versus frequency of hyperbolic times andthe existence of a.c.i.m 4155f|l. Ilyashenko, Minimal attractors 421P» Krauskopf and H.M. Osinga, Geodesic parametrization of globalinvariant manifolds or what does the Equadiff 2003 poster show? . 4294k, Pumarino and J.C. Tatjer, A possible new family oftwo-dimensional strange attractors 434A. Tahzibi, C 1 generic Pesin's entropy formula 440

? • '

Symmetry and mechanics (Org.: M. Golubitsky, M. Robertsand A. Vanderbauwhede) 447

M.A.D. Aguiar, S.B.S.D. Castro and I.S. Labouriau, Switchingtiong a network 449M. Golubitsky and C. Alves-Pinto, Bipedal locomotion 452SLB.S.D. Castro and A.A. du Plessis, Intrinsic complete transversalsand the recognition of equivariant bifurcations 458j ; Galan-Vioque, F.J. Mufioz-Almaraz and E. Freire, Stability andbifurcation behavior of the figure eight solution of the threebody problem 464S.V. Golovin, On the group-invariant solutions ofthe gas dynamics equations 470D. Gomez, M. Lobo and E. Perez, Vibrating plates with concentratedmasses and very small thickness: Low frequencies 473H. Hanfimann and J.C. van der Meer, On non-degenerateHamiltonian Hopf bifurcations in 3D OF systems 476C. McCord, J. Montaldi, M. Roberts and L. Sbano, Relative periodicOrbits of symmetric Lagrangian systems 482S. Yanchuk and K.R. Schneider, Complete synchronization ofsymmetrically coupled autonomous systems 494

Shock waves and conservation laws(Org.: K. Zumbrunand D. Serre) 497

F. Berthelin and A. Vasseur, From kinetic equations tomultidimensional isentropic gas dynamics 499J.-F. Coulombel and P. Secchi, Stability of compressible vortex sheets 502V.A. Galkin, Singularities of the solution of the infinite-dimensionalhyperbolic smoluchowski system describing coagulation process . . 505J. Harterich, Existence of rollwaves in a viscous shallow water equation 511G. Lyng, K. Zumbrun and H.K. Jenssen, Stability of detonation waves 517F. Rousset, Stability of large Ekman-Hartmann boundary layers . 520

Nonlinear elliptic partial differential equations(Org.: A. Ambrosetti and C. Stuart) 523

P. Caldiroli and R. Musina, On the Dirichlet problem for H-systemson the disc with prescribed mean curvature 525S. Cano-Casanova and J. Lopez-Gomez, Permanence and segregationof species for large interactions in heterogeneous environment . . 531S. Cingolani, On Morse theory for a class of quasilinearelliptic equations involving p-Laplace operator 534E. Colorado and I. Peral, Some results for elliptic eigenvalue problemswith moving mixed boundary conditions 540R. Laister and R.E. Beardmore, Bifurcations in degenerateelliptic equations 546V. Liskevich, S. Lyakhova and V. Moroz, Positive solutions tosemilinear elliptic equations with critical lower order terms . . . 549Y. Naito, A variational approach to self-similar solutionsfor semilinear heat equations 555S. Stingelin, Multiple positive solutions for the Brezis-Nirenbergproblem on the sphere S" 558Z.-Q. Wang, Minimax method, invariant sets, and applications tonodal solutions of nonlinear elliptic problems 561

Algebraic aspects and optimisation in dynamical systems(Org.: O.J. Vrieze, R.L.M. Peeters and H.Th. Jongen) 567

M. Bartkiewicz and S. Walczak, Optimal control of systemswith periodic and Dirichlet boundary conditions 569

tt.L.M. Peeters and B. Hanzon, On the Riemannian manifold0$ucture of classes of linear systems 575|WLM. Peeters and B. Hanzon, Identifiability of homogeneouspolynomial systems using the state isomorphism approach . . . . 581Jf»G. Willems and P. Rapisarda, Balanced state representations fromkigher-order models 587

Case s tudies in theoret ical in te rpre ta t ion of numericalexperiments (C. Simo and H. Broer) 593

|jkW. Broer, M. van Noort and C. Simo, Existence and measure&f 2-quasiperiodicity in Hamiltonian one-and-a-half degree of freedomkystems 595H.W. Broer, C. Simo and R. Vitolo, Quasi-periodic Henon-likeattractors in the Lorenz-84 climate model with seasonal forcing . . 601iC< Green and B. Krauskopf, Sudden transitions to chaos in atemiconductor laser with optical delay 607

h A. Gaunersdorfer, C.H. Hommes and F.O.O. Wagener, Nonlocal onsetof instability in an asset pricing model with heterogeneous agents . 613A. Jorba and J.C. Tatjer, On the fractalization of invariant curves 619I . Sanchez, B. Garcia-Archilla, M. Net and C. Simo, Continuation ofperiodic orbits in large-scale dissipative systems 625C. Simo, On the use of Lyapunov exponents to detect global propertiesof the dynamics 631

Infinite-dimensional dynamics (Org.: B . Fiedlerand G. Raugel) 637

G. Bellettini and G. Fusco, A regularized Perona-Malik functional:some aspects of the gradient dynamics 639I.D. Chueshov and A.M. Rekalo, Long-time dynamics offmetion-diffusion equations on thin two-layer domains 645M. Georgi and N. Jangle, Spiral wave motion in reaction-diffusionsystems 651Z. Galias, Krawczyk method for proving the existence of periodic

orbits of infinite dimensional discrete dynamical systems . . . . 657

H. Petzeltova, Convergence of solutions of a non-local phase-field

system with memory 663

R. Orive, Weakly nonlinear long-time behavior of solutions to ahyperbolic relaxation systems 666C. Rocha, Transversality in semilinear parabolic equations on the circle 672M. Wolfrum, The concept of adjacency for stationary andnon-stationary solutions of scalar semilinear parabolic PDE . . . 678

Quasiperiodicity (Org.: H. Hanfimann and H. Broer) 685

S. Abenda and Y. Fedorov, Integrable ellipsoidal billiards withseparable polynomial potentials 687A. Berger, Dynamics and digits: on the ubiquity of Benford's law . 693H.W. Broer, R.H. Cushman and F. Fasso, A Hamiltonian KAMtheorem for bundles of Lagrangean tori 696H.W. Broer, H. Hanfimann, A. Jorba, J. Villanueva andF. Wagener, Quasi-periodic response solutions at normal-internalresonances 702H.W. Broer, J. Hoo and V. Naudot, Normal linear stability ofquasi-periodic tori in the Hamiltonian 1 : — 1 resonance case . . . 708H.W. Broer, V. Naudot and R. Roussarie, Extension ofcatastrophe theory to Dulac unfoldings 714M.C. Ciocci, Persistence of quasi periodic orbits in families ofreversible systems with a 1 : 1 resonance 720H.S. Dumas and J.A. Ellison, Averaging for quasiperiodic systems 726H. Hanfimann, Hamiltonian bifurcations of invariant tori with avanishing Floquet exponent 732A. Litvak-Hinenzon, The mechanism of parabolic resonance orbits 738

Delay equations (J. Mallet-Paret and H.O. Walther) 745

T. Caraballo, M.J. Garrido-Atienza and B. Schmalfuss, On the stabilityof stationary solutions of stochastic evolution equations with delays 747G. Derfel, How small can a "small solution" be? 750T. Erneux, L. Larger, K. Green and D. Roose, Modelling nonlinearoptics phenomena using delay differential equations 756T.Luzyanina and D. Roose, Approximation of the characteristicroots of integral equations with distributed delays 762J. Sieber and B. Krauskopf, Dynamics of an inverted pendulumsubject to delayed control 768

Wave stability and pattern formation (Org.: A. DoelmanAnd B. Sandstede) 775

L. Brusch, H.K. Park, M. Bar and A. Torcini, Spiral instabilities inperiodically forced extended oscillatory media 777A. Doelman, D. Iron and Y. Nishiura, Edge bifurcations insingularly perturbed reaction-diffusion equations: a case study . . 783F. Hamel, Propagation phenomena for KPP-type equations inunbounded domains 789L. Malaguti, C. Marcelli and S. Matucci, The effects of convectiveprocesses on front propagation in various reaction-diffusion equations 795L.M. Lerman and and L.A. Belyakov, Stationary localized solutions,fronts, and traveling fronts to the generalized ID Swift-Hohenberg

equation 801H. Susanto and S.A. van Gils, Semifluxons in a long Josephsonjunction with a TT-discontinuity point 807J. Wei and M. Winter, Existence and stability of multiplespot solutions for the Gray-Scott model in R2 813

Nonautonomous dynamics (Org.: R. Johnson, R. Obaya,G. Sell and Y. Yi) 819

J. Andres , Sharkovskii's theorem and differential equations . . . . 821T . Carabal lo a n d J. R e a l , Asymptotic behaviour and attractorsof 2D-Navier-Stokes models with delays 827D. Cheban and C. Mammana, Invariant manifolds, global attractorsand almost periodic solutions of non-autonomous difference equations 833R. Fabbri and R. Johnson, On a saddle-node bifurcation in aproblem of quasi-periodic harmonic forcing 839C. Nunez and R. Obaya, Uniform complete guiding sets forfinite-delay differential equations 848J. Puig and C. Simo, The spectrum of Schrodinger operatorswith quasi-periodic potential: a dynamical approach 856

Normal forms and invariant manifolds (Org.: P. Bonckaertand F. Verhulst) 863

P. Bonckaert and E. Fontich, Invariant manifolds of near rotationmaps 865

P. Collins and B. Krauskopf, Chaotic lasers: manifolds, bifurcationsand symbolic dynamics 871E. Fontich, R. de la Llave and P. Martin, Non-resonant invariantmanifolds in non-uniformly hyperbolic systems 877M . M e s s i a s , R e s o n a n c e s and s u b h a r m o n i c bifurcations of largea m p l i t u d e p e r i o d i c o r b i t s of p l a n a r p o l y n o m i a l v e c t o r fields . . . . 8 8 0

Singular perturbations (Org.: T. Kaper, S. Szmolyan andF. Dumortier) 887

V. Gelfreich and L.M. Lerman, Slow manifolds in a singularlyperturbed Hamiltonian system 889A. Huber, Dynamics on different time scales in the Yamada model 895P. De Maesschalck and F. Dumortier, Canard solutions at nongenericturning points 898A.I. Neishtadt, On accuracy of the averaging method in two-frequencysystems with small Hamiltonian and much smallernon-Hamiltonian perturbations 904H. Oka, Conley index theory for slow-fast systems: multi-dimensionalslow manifold 910N. Popovic, A geometric analysis of the Lagerstrom model:existence of solutions and rigorous asymptotic expansions . . . . 916B. Schmalfuss and K.R. Schneider, Existence of a slow invariantmanifold for a class of random differential equations with two timescales 919E.V. Shchetinina, Loss of stability scenario in the Ziegler system . 922M. Wechselberger, Poincare maps for relaxation oscillations inM.3-invariant manifolds, canards and turning points 925W. Weckesser, Canards and horseshoes in the forced van der Polequation 931

Differential geometric foliations and flows(Org.: J. Sotomayor) 937

R. Garcia, L.F. Mello and J. Sotomayor, Principal mean curvaturefoliations on surfaces immersed inB.4 939L. F. Mello, Line fields on surfaces immersed in R4 951B. Smyth, The nature of elliptic sectors in the principal foliations ofsurface theory 957

loclinic and heteroclinic dynamics (Org.: H. KokuboA.J. Homburg) 961

i.3. Homburg and J. Knobloch, Bellows bifurcating from degenerateclinic orbits in conservative systems 963

. Gonzalez, Topological classification for multipleHe-connections 972

, Ibanez and J.A. Rodriguez, Shil'nikov homoclinic orbits in the\ ^folding of a codimension-3 singularity 975

£. Wagenknecht, The reversible homoclinic pitchfork bifurcationttisited 978

;' JEC Yagasaki, Detection of homoclinic and heteroclinic behavior insflamiltonian systems with saddle-centers 984

, ^Mathematical aspects of celestical mechanics! |Org.: A. Albouy and R. Moeckell) 991

Hampton, Co-circular central configurations in the four-body993

i T., Kapela, N-BODY choreographies with a reflectional symmetry -fpmputer assisted existence proofs 999

f. R. Martinez, A. Sama and C. Simo, Stability of homographic solutionshe planar three-body problem with homogeneous potentials . 1005

I p. Offin and J. Grand'maison, Symmetric periodic orbits in thethree body problem 1011

I Contributed talks 1019

IkA.B. Alshin, M.O. Korpusov, Yu.D. Pletner and A.G. Sveshnikov,

U 0ew Sobolev equations and dynamical potentials 1021•A.B. Alshin, E.A. Alshina and N.N. Kalitkin, Application ofguasi-uniform grids for numerical solution of initial-boundary valuepp&iems in unbounded domain 1024F.M. Atay, Stability of coupled delay differential equationsfleer Hopf bifurcation 1027A. Afendikov, Properties of 2D Navier-Stokes flow in infinite stripfor spatially non-decaying initial data 1030

A. Boichuk, Perturbed Fredholm BVP's for delay differential systems 1033M. Camarinha and L. Abrunheiro, Cubic polynomials on SO(3) 1036N. Chernyavskaya and L. Shuster, On a problem ofHartman-Wintner for difference equations 1039T. Caraballo, P. Marln-Rubio and J. Valero, Attractors of delayeddifferential equations without uniqueness 1042P.S. Casas and A. Jorba, Unstable manifolds computation for thetwo-dimensional plane Poiseuille flow 1045A. Cernea, Some qualitative properties of solutions to nonconvexhyperbolic differential inclusions 1048Y. Cheng and L. Wang, Remarks on bifurcation in elliptic boundaryvalue problems 1051J.I. Diaz and L. Tello, On a parabolic problem with diffusionon the boundary arising in climatology 1056A. Domoshnitsky, On stability of nonautonomous integro-differentialequations 1059A. A. Egorov, Stability of classes of solutions to partial differentialrelations constructed by quasiconvex functions and null lagrangians 1065J.Z. Farkas, Stability of equilibria of a non-linear populationdynamical model 1068V.A. Gaiko and W.T. van Horssen, Global analysis of a canonicalcubic system 1071H. Gilsing, On Cp -stability of numerical schemes for linear stochasticdelay differential equations 1074M. Guzman-Gomez, Asymptotic behavior of solutions to theZakharov system 1080S.C. Hille, Review of mathematical modelling in the study ofcollective movement of Dictyostelium discoideum 1083J. Horak, Constrained mountain pass algorithm 1086D. Horstmann, Forward-backward parabolic equations and theirtime delay approximations 1089F. Izsak, Volterra integrodifferential equations with infinite delay 1092H. Kantz and V. Reitmann, Determining functionals for bifurcationson a finite-time interval in variational inequalities 1098N.A. Karazeeva, Approximations of the equations describingmotions of bingham fluids 1101N.B. Konyukhova, A.L. Dyshko and N.A. Voronov, Singularproblems for self-similar solutions to the systems of nonlinear waveequationsin the inflationary cosmology 1105

H. Lumbantobing and T.I. Haaker, Quenching of aeroelasticoscillations of a seesaw oscillator by means of a dynamic absorber 1108J.J. Miguel, A. Shindiapin and A. Ponosov, Stability and linearchain trick 1111B. Oldeman and B. Krauskopf, A vector field model of a saddle-nodeHopf bifurcation with global reinjection 1114G . S . O s i p e n k o , Hyperbolicity t e s t and s t r u c t u r a l s t a b i l i t y . . . . 1 1 1 7P.G. Papadopoulos and N.M. Stavrakakis, Global existence,blow up and asymptotic results for kirchhoff strings on R N . . . 1122A. R o d k i n a , On stability of stochastic nonlinear non-autonomoussystems with delay 1 1 2 5K. Saxton and R. Saxton, Phase transitions and aspects of heatpropagation in low temperature solids 1128Tadie, Existence and structure of singular solutions forAU = {U -c)p

+, p> 1 mM n 1131Tadie, Lower bounds for large solutions of some anisotropic problemsin regular bounded domains 1134A. Tertikas and N.B. Zographopoulos, Optimizing improved Hardyinequalities for the biharmonic operator 1137H. Usami, Existence of positive decaying solutions of singularquasilinear ordinary differential equations 1140W.T. van Horssen, On asymptotics for weakly nonlinear wave,beam, and plate equations 1143S.B. Waluya and W.T. van Horssen, On asymptotic approximationsof first integrals for a strongly nonlinear forced oscillator . . . 1146K. Wojteczek, Classes of functions fulfilling second order Hardy typeintegral inequalities on the example of 'standard' Hardy inequality 1149M.A. Zarubinskaya and W.T. van Horssen, On the vibrations of asimply supported square plate on a weakly nonlinear elasticfoundation 1152

Author Index 1155