Table of contents for Concepts and results in chaotic dynamics : a short course / Pierre Collet, Jean-Pierre Eckmann.


Bibliographic record and links to related information available from the Library of Congress catalog
Note: Electronic data is machine generated. May be incomplete or contain other coding.


Counter
1   A Basic Problem   ....    .      ...,,          .. .   . .. . . . . .  1
2   Dynamical Systems       .....                    ..               5
2.1 Basic of Mechanical Systems     .....      .   ..       .     5
22   Formal Definitions  . ...   .     .   .   . ..         .    10
2.   Maps ....   .......                ....  .     .11
2 4  Basic Examples of Maps ......              ......           12
2 5  More Advanced Examples   . . .   ...   .              . .   17
26   Examples of Flows                 .   .   .....      ..     23
3   Topological Properties            .           .*. . . .. ...     27
3.1 Coding Kneading                   .      .     .   .         27
312  Topological Entropy ..  . ..     . ..                 . ..  30
3.2.1  Topological, Measure, and Metric Spaces  ........    30
3 2.2  Some Examales .    ....      .......       ....      30
3.2.3  General Theory of Topological Entropy .....          32
3.2 .4  A Metric Version of Topological Entropy  .........  34
3 3  Attractors       ........ .......                           38
4   Hyperbolicity.....               ...           .    ".......     45
4.1 Hyperbolic Fixed Points  .......                ....     .   46
4 1i1  Stable and Unstable Manifolds  .      ......         49
41 .2  Conjugation . .   ........ .                   .     53
4 1 .3  Resonances ..  .....                      .         58
4.2  nvariant Manifolds.                                         60.
4.3  Nonwandering Points and Axiom A Systems          ....       63
4 4  Shadowing and Its Consequences  ....65
4.4 .1 Sensitive Dependence on Initial Conditions..  .....   69
4 4 2  Complicated Orbits Occur in Hyperbolic Systems .........69
4 4.3  Change of Map .. ....       ....      ...            70
4.5  Constructi on of Makox Partitions .... .  .....             72
S Invariant Measures ..   ..         .......  . .. . . .          79
5  1  Ove  .iew ..  . .  ...  .  .. .11 - 1 -  . ...... .  .....  . ...  79
5.2  D eta~lnil s.  .              ....  . -  . .... . -.... ..... ..  .  ... . . .  . . ... .  85
5.3  The Perron-Frobenius Operator .... .... .......              89
5.4   he rgodi Theorem     ......                                 93
5 5  Convergence Rates in the Ergoic Theorem. .  ......   .  ... 103
5 6  \hxing and Decay of Correlations ............     . . ...... 105
5 7  Physical Measures ..  .....  .. .    .   .   ..     . .     114
5.8  Iyapunov Exponents.....    .  ......              .  . ..   116
6.1 The Shannon-McMillan-Biman Theorem       ........   ....     125
6 2  SinaiBowen-Ruelle Measues . .   .                            130
6 3  Dimensions     . .. .    ....                               132
"7  Statistics and Statistical Mechanics   . .. .      .      .. .  .  41
7 1  The Central Lim t Theorem ....... ......    .....           141
7.2  Large Deviations                                            147
73  LExponential Estimates.............................          149
731    Concentration  ..  ..... ...                          151
7.4  The Fo malism of Statistical Mechanics ... .. ..  . . . . . 153
7.5  Multifracal Meaures   .    .   . ..                         156
ther Probabilisti.                .   .  .. ..     ......   ..        163
8.1 iEntrance and Recurrence Times   . .....  . . .  ..... .      163
8 2  Number of Visits to a Set  .                                 72
8.3  Extremes.         ..         ....   . ....      .           173
8.4  Quasi-Invariant Measures  .. . .  . . . . .        .....    175
8.5  Stochatic Prtu   tions.....                        .        178
9   Experimental Aspects ..... ..   . ..   . ... ..... . ..... .. . ..  187
9.1  Correlation Functions and PoweT Spectrum ...     ..    .... ... 188
9.2  Resonances   .  .  ..  .... . . . ..  . . .  . .  .. .  ...  . .  .  . .  ..  191
9.3  Lyapunov Exponents.  . ........ ....... . ... . . . ... .   196
9.4  Reconstuction ..       .......        .......               20
9.5  Measuring the yapunov Exponents . .   . ... ...  .    .     205
9.6  Measuring Dimensions ..     .                               206
9.7  Measuring Entropy . . .   ..     . ..    ....   . . .     .  21
9.8  Estimating the Invariant Measure   . ... . ...              211



Library of Congress subject headings for this publication: Differentiable dynamical systems