Sergei Yu Pilyugin's Books

Shadowing and Hyperbolicity

By: Sergei Yu Pilyugin,Kazuhiro Sakai

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Focusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this book surveys recent progress in establishing relations between shadowing and such basic notions from the classical theory of structural stability as hyperbolicity and transversality. Special attention is given to the study of "quantitative" shadowing properties, such as Lipschitz shadowing (it is shown that this property is equivalent to structural stability both for diffeomorphisms and smooth flows), and to the passage to robust shadowing (which is also equivalent to structural stability in the case of diffeomorphisms, while the situation becomes more complicated in the case of flows). Relations between the shadowing property of diffeomorphisms on their chain transitive sets and the hyperbolicity of such sets are also described. The book will allow young researchers in the field of dynamical systems to gain a better understanding of new ideas in the global qualitative theory. It will also be of interest to specialists in dynamical systems and their applications.

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Page Count

228

Publisher

Springer

Published Date

ISBN 10

3319651846

ISBN 13

9783319651842

Shadowing in Dynamical Systems

By: Sergei Yu. Pilyugin

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Shadowing in Dynamical Systems

By: Sergei Yu. Pilyugin

This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.

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284

Publisher

Springer

Published Date

ISBN 10

3540484299

ISBN 13

9783540484295

The Space of Dynamical Systems with the C0-Topology

By: Sergei Yu. Pilyugin

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The Space of Dynamical Systems with the C0-Topology

By: Sergei Yu. Pilyugin

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.

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Page Count

197

Publisher

Springer

Published Date

ISBN 10

3540483144

ISBN 13

9783540483144

Introduction to Structurally Stable Systems of Differential Equations

By: Sergei Yurievitch Pilyugin

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Introduction to Structurally Stable Systems of Differential Equations

By: Sergei Yurievitch Pilyugin

1. Flows and Cascades.- 2. Equivalence Relations.- 3. Spaces of Systems of Differential Equations and of Diffeomorphisms.- 4. Hyperbolic Rest Point.- 5. Periodic Point and Closed Trajectory.- 6. Transversality.- 7. The Kupka-Smale Theorem.- 8. The Closing Lemma.- 9. Necessary Conditions for Structural Stability.- 10. Homoclinic Point.- 11. Morse-Smale Systems.- 12. Hyperbolic Sets.- 13. The Analytic Strong Transversality Condition.- Appendix. Proof of the Grobman-Hartman Theorem.- References.

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Page Count

208

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764325747

ISBN 13

9783764325749

Spaces of Dynamical Systems

By: Sergei Yu. Pilyugin

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Spaces of Dynamical Systems

By: Sergei Yu. Pilyugin

Dynamical systems are abundant in theoretical physics and engineering. Their understanding, with sufficient mathematical rigor, is vital to solving many problems. This work conveys the modern theory of dynamical systems in a didactically developed fashion. In addition to topological dynamics, structural stability and chaotic dynamics, also generic properties and pseudotrajectories are covered, as well as nonlinearity. The author is an experienced book writer and his work is based on years of teaching.

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Page Count

248

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110258412

ISBN 13

9783110258417

Shadowing in Dynamical Systems

By: Sergei Yu. Pilyugin

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Shadowing in Dynamical Systems

By: Sergei Yu. Pilyugin

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Solve jigsaw puzzle

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Page Count

284

Publisher

Springer

Published Date

ISBN 10

3540484299

ISBN 13

9783540484295

Shadowing and Hyperbolicity

By: Sergei Yu Pilyugin,Kazuhiro Sakai

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Shadowing and Hyperbolicity

By: Sergei Yu Pilyugin,Kazuhiro Sakai

Average ratings

N/A

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Solve jigsaw puzzle

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Page Count

228

Publisher

Springer

Published Date

ISBN 10

3319651846

ISBN 13

9783319651842

Book's by Sergei Yu Pilyugin

Shadowing and Hyperbolicity

Shadowing and Hyperbolicity

Shadowing in Dynamical Systems

Shadowing in Dynamical Systems

The Space of Dynamical Systems with the C0-Topology

The Space of Dynamical Systems with the C0-Topology

Introduction to Structurally Stable Systems of Differential Equations

Introduction to Structurally Stable Systems of Differential Equations

Spaces of Dynamical Systems

Spaces of Dynamical Systems

Shadowing in Dynamical Systems

Shadowing in Dynamical Systems

Shadowing and Hyperbolicity

Shadowing and Hyperbolicity

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