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web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic

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Page 1: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 2: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 3: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 4: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 5: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 6: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 7: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 8: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 9: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 10: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 11: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 12: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 13: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 14: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 15: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 16: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 17: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 18: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 19: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 20: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic
Page 21: web.ma.utexas.edu · APERIODIC TILINGS, ERGODIC THEORY, AND ROTATIONS CHARLES RADIN Department of Mathematics University of Texas Austin, TX 78712-1082, USA Abstract We use ergodic

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