Shadowing In Dynamical Systems

Author: Sergei Yu. Pilyugin
Publisher: Springer
ISBN: 3540484299
File Size: 44,43 MB
Format: PDF, Docs
Read: 2644
Download or Read Book

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.

Shadowing In Dynamical Systems

Author: K.J. Palmer
Publisher: Springer Science & Business Media
ISBN: 1475732104
File Size: 43,94 MB
Format: PDF, ePub, Docs
Read: 5529
Download or Read Book

In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.

Differentiable Dynamical Systems

Author: Lan Wen
Publisher: American Mathematical Soc.
ISBN: 1470427990
File Size: 19,37 MB
Format: PDF, ePub
Read: 8311
Download or Read Book

This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.

Six Lectures On Dynamical Systems

Author: Bernd Aulbach
Publisher: World Scientific
ISBN: 9789810225483
File Size: 79,53 MB
Format: PDF, ePub, Docs
Read: 2465
Download or Read Book

This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included.The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level.

Shadowing And Hyperbolicity

Author: Sergei Yu Pilyugin
Publisher: Springer
ISBN: 3319651846
File Size: 24,54 MB
Format: PDF, Kindle
Read: 6422
Download or Read Book

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.

Discrete And Continuous Dynamical Systems

Author:
Publisher:
ISBN:
File Size: 74,54 MB
Format: PDF, Mobi
Read: 8581
Download or Read Book


Differential Equations

Author: K.D. Elworthy
Publisher: Routledge
ISBN: 1351455206
File Size: 56,66 MB
Format: PDF, Docs
Read: 7501
Download or Read Book

Presents recent developments in the areas of differential equations, dynamical systems, and control of finke and infinite dimensional systems. Focuses on current trends in differential equations and dynamical system research-from Darameterdependence of solutions to robui control laws for inflnite dimensional systems.

St Petersburg Mathematical Journal

Author:
Publisher:
ISBN:
File Size: 80,20 MB
Format: PDF, Docs
Read: 3158
Download or Read Book


Chinese Journal Of Contemporary Mathematics

Author:
Publisher:
ISBN:
File Size: 11,63 MB
Format: PDF, ePub, Docs
Read: 7580
Download or Read Book


Spaces Of Dynamical Systems

Author: Sergei Yu. Pilyugin
Publisher: Walter de Gruyter
ISBN: 3110258412
File Size: 19,52 MB
Format: PDF, ePub, Docs
Read: 9939
Download or Read Book

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.