Click here to load reader

-$3*/+7&>/$8$:?@&A$8B&CD@&E$B&F&5G3(B@&HIIH6@&..B&JIK,ILF ...people.kzoo.edu/barth/math280/articles/chaos3specis.pdf · 7'(7'(4(.'(?(b(&(B(/(^()(K

  • Upload
    others

  • View
    9

  • Download
    0

Embed Size (px)

Citation preview

  • !"#$%&'(&)"*++,-.+/'+%&0$$1&!"#'(234"$*5%67&28#(&9#%4'(:%(1&)"$;#%&/$8$:?@&A$8B&CD@&E$B&F&5G3(B@&HIIH6@&..B&JIK,ILF

  • !"#$#%&'()*+,-'(.//.'(001(2/34/5,(6,(.//.(7&(89:(!"#$#%;"(B#AQ;

  • dRQ:(.//.( BC?D=( EF(?(GCH!!4=I!BE!=( JDDK( BC?EF( 2/)(

    P0:";:P(e(

    P0:";:P(f(

    P0:";:P(g(JEN1(.1( G9:(>::S;Q%(A:$##S("9A#@(0A:&(8#(0A:S##S("9#A8P'(Y:($:8(e(7:(89:(QR@7:AP(#>(89:(P0:";:P((89:(>##S("9#A(;(i( .'(*( +*-(

    A:0A:P:Q8;Q%(89:(>RQ"8;#Q*+&-^(4( S$&(S^hS8(i(>*+&-^(4( S*^( +c-(

    Y;89(

    >+R-( i(

  • 2/2( ?M?F(C?=GEFN=( ?FK( GCDV?=( IDW!MM( !"#$#%&'(k#$1()*'(F#1(,(

  • dRQ:(.//.( BC?D=( EF(?(GCH!!4=I!BE!=( JDDK( BC?EF( 2//(

    512(

    5( 8( n4( 4( A4( 4(5( .55( *55( ,55( c55( U55(

    8;@:(JEN1(,1( K;O:A%:Q":(#>(8A:A:Q8(;Q;8;>:AP(>A#@(89:(>;AP8(7&("9>:A:Q8(;Q;8;A#@(,1*(8#(31*'("9

  • /55( ?M?F(C?=GEFN=( ?FK( GCDV?=( IDW!MM( !"#$#%&'(k#$1()*'(F#1(,(

    ?$P#'(>A#@(J;%1(cB(Y:("RA89:A(:X#A(P#@:(P:$:"8:S(O(7'(7&("#QP8AR"8;Q%(RQ"8;#QA:]R:Q";:P(;QS(@:(

  • dRQ:(.//.( BC?D=( EF(?(GCH!!4=I!BE!=( JDDK( BC?EF( /5.(

    ?( b( nnnnnnnnnnnnnnnnnn51/2(?(b^( e(515,U( 5( 11(

    51/)(&+Q-( 1( XnQ-(515*U( 51/3(

    FPp51/U4( 4( h( \( q5r(

    515.U4( E( E( 51/U( E( E( E(51/U( 51/3( 51/)( 51/2( 51/U( 51/3( 51/)( 51/2(

    X+Q-( X+Q-(

    K(51//( 1Z( 11q(

    5152nnnnnnF(

    &+Q-(p( 1( J$(51/)(515c( XQ( -(

    F( nnnnnnn51/U(

    5( E51/,(51/,( 51/U( 51/)( 51//( 51/,( 51/U( 51/)( 51//(

    X(+Q-( X(+Q-(

    I#;Q"

  • /5*( ?M?F(C?=GEFN=( ?FK( GCDV?=( IDW!MM( !"#$#%&'(k#$1()*'(F#1(,(

    #>(X'(&'(:"8P(#>(P:QP;8;O;8&(8#(;Q;8;##S4Y:7(P8AR"4(8RA:1(!"#$#%&(32[.2),4.2)31(JA#P8'(b1(W1( ./2)1( NA

  • dRQ:(.//.( BC?D=( EF(?(GCH!!4=I!BE!=( JDDK( BC?EF( /5,(

    G9#@0P#Q'(