前辅文
 1 Introductio
  1.1 Initial Concept
  1.2 Summar
 2 One-Dimensional Mapping
  2.1 Introduction
  2.2 The Concept of Stability
   2.2.1 Asymptotically Stable Fixed Poin
   2.2.2 Neutral Stability
   2.2.3 Unstable Fixed Poin
  2.3 Fixed Points to the LogisticMap
  2.4 Bifurcations
   2.4.1 Transcritical Bifurcation
   2.4.2 Period Doubling Bifurcatio
   2.4.3 Tangent Bifurcatio
  2.5 Summar
  2.6 Exercise
 3 Some Dynamical Properties for the Logistic Ma
  3.1 Convergence to the Stationary Stat
   3.1.1 Transcritical Bifurcation
   3.1.2 Period Doubling Bifurcatio
   3.1.3 Route to Chaos via Period Doublin
   3.1.4 Tangent Bifurcatio
  3.2 Lyapunov Exponen
  3.3 Summar
  3.4 Exercise
 4 The Logistic-Like Map
  4.1 The Mappin
  4.2 Transcritical Bifurcatio
   4.2.1 Analytical Approach to Obtain α, β, z and δ
   4.2.2 Critical Exponents for the Period Doubling Bifurcatio
  4.3 Extensions to Other Mapping
   4.3.1 Hassell Mapping
   4.3.2 Maynard Mappin
  4.4 Summar
  4.5 Exercise
 5 Introduction to Two Dimensional Mappings
  5.1 Linear Mapping
  5.2 Nonlinear Mapping
  5.3 Applications of Two Dimensional Mapping
   5.3.1 Hénon Ma
   5.3.2 Lyapunov Exponent
   5.3.3 IkedaMap
  5.4 Summar
  5.5 Exercise
 6 A Fermi Accelerator Mode
  6.1 Fermi-Ulam Model
   6.1.1 Jacobian Matrix for the Indirect Collision
   6.1.2 Jacobian Matrix for the Direct Collision
   6.1.3 Fixed Point
   6.1.4 Phase Spac
   6.1.5 Phase Space Measure Preservatio
  6.2 A Simplified Version of the Fermi-Ulam Model
  6.3 Scaling Properties for the Chaotic Se
  6.4 Localization of the First Invariant Spanning Curv
  6.5 The Regime of Growt
  6.6 Summar
  6.7 Exercise
 7 Dissipation in the Fermi-Ulam Model
  7.1 Dissipation via Inelastic Collision
   7.1.1 Jacobian Matrix for the Direct Collision
   7.1.2 Jacobian Matrix for the Indirect Collision
   7.1.3 The Phase Space
   7.1.4 Fixed Point
   7.1.5 Construction of theManifolds
   7.1.6 Transient and Manifold Crossings Determinatio
   7.1.7 Determining the Exponent δ from the Eigenvalues of the Saddle Poin
  7.2 Dissipation by Drag Force
   7.2.1 Drag Force of the Type F = −˜η
   7.2.2 Drag Force of the Type F = ±˜η
   7.2.3 Drag Force of the Type F = −˜ηv
  7.3 Summar
  7.4 Exercise
 8 Dynamical Properties for a Bouncer Model
  8.1 The Model
  8.2 Complete Version of the Bouncer Model
   8.2.1 Successive Collision
   8.2.2 Indirect Collision
   8.2.3 Jacobian Matrix
   8.2.4 The Phase Space
  8.3 A Simplified Version of the Bouncer Mode
  8.4 Numerical Investigation on the Simplified Versio
  8.5 Approximation of Continuum Tim
  8.6 Summar
  8.7 Exercise
 9 Localization of Invariant Spanning Curves
  9.1 The Standard Mappin
  9.2 Localization of the Curves
  9.3 Rescale in the Phase Spac
  9.4 Summar
  9.5 Exercise
 10 Chaotic Diffusion in Non-Dissipative Mapping
  10.1 A Family of Discrete Mappings
  10.2 Dynamical Properties for the Chaotic Sea:A Phenomenological Description
  10.3 A Semi Phenomenological Approac
  10.4 Determination of the Probability via the Solution of the Diffusion Equation
  10.5 Summar
  10.6 Exercise
 11 Scaling on a Dissipative Standard Mapping
  11.1 The Model
  11.2 A Solution for the Diffusion Equatio
  11.3 Specific Limit
  11.4 Summar
  11.5 Exercise
 12 Introduction to Billiard Dynamic
  12.1 The Billiard
   12.1.1 The Circle Billiar
   12.1.2 The Elliptical Billiar
   12.1.3 The Oval Billiard
  12.2 Summar
  12.3 Exercise
 13 Time Dependent Billiard
  13.1 The Billiard
   13.1.1 The LRA Conjectur
  13.2 The Time Dependent Elliptical Billiard
  13.3 The Oval Billiar
  13.4 Summar
  13.5 Exercise
 14 Suppression of Fermi Acceleration in the Oval Billiar
  14.1 The Model and the Mappin
  14.2 Results for the Case of F ∝ −V
  14.3 Results for the Case of F ∝ ±V2
  14.4 Results for the Case of F ∝ −Vδ
  14.5 Summar
  14.6 Exercise
 15 A Thermodynamic Model for Time Dependent Billiards
  15.1 Motivation
  15.2 Heat Transference
  15.3 The Billiard Formalis
   15.3.1 Stationary Estate
   15.3.2 Dynamical Regim
   15.3.3 Numerical Simulations
   15.3.4 Average Velocity over n
   15.3.5 Critical Exponent
   15.3.6 Distribution of Velocitie
  15.4 Connection Between the Two Formalis
  15.5 Summar
  15.6 Exercise
 Appendix A: Expressions for the Coefficients
 Appendix B: Change of Referential Frame
 Appendix C: Solution of the Diffusion Equation
 Appendix D: Heat Flow Equatio
 Appendix E: Connection Between t and n in a Time Dependent Oval Billiar
 Appendix F: Solution of the Integral to Obtain the Relation Between n and t in the Time Dependent Oval Billiard
 Bibliograph