Billiards

Based on the file with md5=FE43763637FC51932F0CEA20AB15E533, the contents/outline/bookmark is added by using MasterPDF(free version). It seems that the figure on page 104 is missing. cover abs CONTENTS INTRODUCTION 1. GENERAL THEORY AND MATHEMATICAL BACKGROUND 1.1 Mathematical Billiards. Phase and Configuration Spaces 1.2 Invariant Measure and Generating Function for Plane Billiards. Variational Formulation 1.3 Billiard Transformation of the Space of Rays in the Plane 1.4 Language of Symplectic Geometry 1.5 Symplectic Properties of Billiards 1.6 Poincare’s Recurrence Theorem 1.7 Billiard Transformation Revisited : Measure-Theoretic View-Point 1.8 Complete Integrability and the Arnold–Liouville Theorem 1.9 On KAM Theory 1.10 Stochastic Properties of Dynamical Systems 1.11 Entropy 2. CONVEX BILLIARDS 2.1 An Excursion to Elementary Geometry. Billiards in Conics 2.2 Three Geometrical Applications 2.3 Geodesic Flow and Billiards in Ellipsoids 2.4 Birkhoff’s Conjecture 2.5 Periodic Trajectories 2.6 Periodic Trajectories, Poincar ́e’s Last Geometric Theorem and Symplectic Topology 2.7 Length Spectrum and Laplace Operator 2.8 Existence of Caustics 2.9 Twist Maps, Birkhoff’s Theorem and Nonexistence of Caustics 2.10 Aubry-Mather Theory 2.11 Miscellanea 3. BILLIARDS IN POLYGONS 3.1 Square Billiards 3.2 Symbolic Description of Billiards in Squares and Cubes 3.3 Unfolding Trajectories in General Polygons 3.4 Rational Polygons 3.5 Rational Billiards and Quadratic Differentials 3.6 Miscellanea 4. DUAL BILLIARDS 4.1 Definition, Area-Preserving Property and Generating Function 4.2 Invariant Curves, Integrability, Area Spectrum 4.3 Poncelet’s Theorem 4.4 Polygonal Dual Billiards 4.5 Higher-Dimensional Dual Billiards 5. HYPERBOLIC BILLIARDS 5.1 Introducing Hyperbolicity 5.2 Dispersing and Semi-Dispersing Billiards 5.3 Hyperbolic Billiards with Focusing Arcs 5.4 Miscellanea Added in Proof BIBLIOGRAPHY INDEX Serge Tabachnikov. Includes Bibliographical References (p. [131]-139) And Index.