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Pilyugin S.Y. — Space of Dynamical Systems with the Co-Topology
Pilyugin S.Y. — Space of Dynamical Systems with the Co-Topology

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Название: Space of Dynamical Systems with the Co-Topology

Автор: Pilyugin S.Y.


This book is an introduction to main methods and principal results in the theory of Co(remark: o is upper index!!)-small perturbations of dynamical systems. It is the first comprehensive treatment of this topic. In particular, Co(upper index!)-generic properties of dynamical systems, topological stability, perturbations of attractors, limit sets of domains are discussed. The book contains some new results (Lipschitz shadowing of pseudotrajectories in structurally stable diffeomorphisms for instance). The aim of the author was to simplify and to "visualize" some basic proofs, so the main part of the book is accessible to graduate students in pure and applied mathematics. The book will also be a basic reference for researchers in various fields of dynamical systems and their applications, especially for those who study attractors or pseudotrajectories generated by numerical methods.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 198

Добавлена в каталог: 04.07.2008

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Предметный указатель
$C^{0}$-closing lemma      10
$C^{0}-\Omega$-explosion      42
$\delta$-trajectory      28
$\epsilon$-tracing      29
$\omega$-limit set of a subset of M      124
$\Omega$-stable diffeomorphism      16
Attractor      87
Axiom A      16
Basic set      16
Basin of attraction      87
Chain prolongation      34
Chain transitive attractor      97
Chain transitive quasi-attractor      97
Chain-recurrent set      42
Complete family of $\delta$-semi-trajectories      179
Embedding      3
Expansive dynamical system      56
Extended orbit      32
Filtration      49
Fine filtration      50
Fine sequence of filtrations      50
Fundamental domain      68
Generalized hyperbolic set (g.h.s.)      144
Generic property      8
Geometric strong transversality condition      18
Global transversal section      84
Handle decomposition      79
Hausdorff metric      5
Hyperbolic set      14
Hyperbolic trajectory      14
Hyperbolic trajectory segment (h.t.s.)      143
Immersion      3
Limit prolongation      40
Local topological stability      58
Lower semi-continuous map      8
Lyapunov metric      15
Lyapunov stable set      87
Max-$\epsilon$-equivalence      25
Min-$\epsilon$-equivalence      25
Morse — Smale diffeomorphism      20
No-cycle condition      18
Nonwandering point      2
Orbital stability      34
Periodic point      2
Permanent periodic orbit      45
Prolongation with respect to the initial point      34
Prolongation with respect to the system      34
Pseudoorbit tracing property (POTP)      29
Pseudotrajectory      28
Quasi-attractor      90
Residual subset      8
Set of weakly nonwandering points      42
Set of weakly periodic points      41
Shadowing property      29
Stability of attractors in Z(M)      91
Stability with respect to permanent perturbations      34
Stable manifold      15
Strong transversality condition (STC)      18
Structurally stable diffeomorphism      16
Tolerance D-stability      23
Tolerance Stability Conjecture      23
Topological $\Omega$-stability      67
Topological conjugacy      55
Topological stability      53
Topologically hyperbolic fixed point      76
Trajectory      1
Trajectory segment      143
Transversal homoclinic contour      166
Unstable manifold      15
Upper semi-continuous map      8
Weak $\epsilon$-tracing      29
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