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Liu P.D., Qian M., Dold A. — Smooth Ergodic Theory of Random Dynamical Systems
Liu P.D., Qian M., Dold A. — Smooth Ergodic Theory of Random Dynamical Systems

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Название: Smooth Ergodic Theory of Random Dynamical Systems

Авторы: Liu P.D., Qian M., Dold A.

Аннотация:

This book studies ergodic-theoretic aspects of random dynamical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynamical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 221

Добавлена в каталог: 02.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{2}$-norm      23 47
$t_{0}$-time-step entropy      124 125
$\chi(U, v)$-invariant      190
$\chi^{+}(M, v)$-invariant      27
$\mathcal{A}$-conditional entropy      10
$\mathcal{A}$-conditional entropy with respect to $\xi$      10
(global) stable manifold      73 121
(global) unstable manifold      136 184 189
Absolutely continuous      2 3 85 196
Adapted Riemannian metric      183
angle      40
Aperture      73
Brownian motion      116
Canonical system of conditional measures      6
Center unstable set      146
Chapman — Kolmogorov equation      110
Conditional entropy      7
Conditional expectation      3
Conditional expectation operator      3
Continuous family of $C^{1}$ embedded k-dimensional discs      64
Convolution semigroup      110
density      92 190
Density point      4
Disintegration      208
Elliptic      118
entropy      7 31 133 187 208
Ergodic      21 28 132
Ergodic decomposition      21 29
Factor-space      6
Family of sample measures      131 187
Feller semigroup      113
fixed      19
Hoelder continuous      73 75
Hyperbolic      183
Hyperbolic attractor      184
Increasing      158
Invariant measure      24 111 130 207
Jacobian      3
Lebesgue space      5
Local stable manifold      64 122
Local unstable manifold      146 195
Lyapunov exponents      37 119 134 187 209
Lyapunov metric      59
Mean conditional entropy      7
Measurable partition      5
Measurable partition subordinate to $W^{s}$-manifolds      93
Measurable partition subordinate to $W^{u}$-manifolds      136 184 189
Multiplicity      37 119 134 187 209
n-point motion      111
Non-degenerate SDE      118
p-th exterior power space      40
Pesin's entropy formula      91 127 137 184 190
Polish space      2
Polish system      207
Probability measure having absolutely continuous conditional measures on $W^{s}$-manifolds      93
Probability measure having absolutely continuous conditional measures on $W^{u}$-manifolds      136 184 189
Radon — Nikodym derivative      2
Random dynamical system      207
Relation number      49
Ruelle's inequality      45 127 201
SBR property      136
Semigroup of linear operators      112
Separable      1
Skew product transformation      207
Stochastic flow of $C^{r}$ diffeomorphisms      110
Stopping (Markov) time      113
Stratonovich stochastic differential equation      116
Strong Markov process      113
Transition probabilities      92 190
Transitivity      7
Transversal      84
Transverse metric      163
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