1 edition of **Shadowing in Dynamical Systems** found in the catalog.

- 142 Want to read
- 40 Currently reading

Published
**2000**
by Springer US in Boston, MA
.

Written in English

- Differential equations,
- Mathematics,
- Electronic data processing

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.

**Edition Notes**

Statement | by Ken Palmer |

Series | Mathematics and Its Applications -- 501, Mathematics and Its Applications -- 501 |

Classifications | |
---|---|

LC Classifications | QA372 |

The Physical Object | |

Format | [electronic resource] : |

Pagination | 1 online resource (xiv, 299 p.) |

Number of Pages | 299 |

ID Numbers | |

Open Library | OL27087349M |

ISBN 10 | 1441948279, 1475732104 |

ISBN 10 | 9781441948274, 9781475732108 |

OCLC/WorldCa | 851819299 |

This paper is devoted to the existence of a true random periodic solution near the numerical approximate one for a kind of stochastic differential equations. A general finite-time random periodic shadowing theorem is proposed for the random dynamical systems generated by some stochastic differential equations under appropriate conditions and an estimate of shadowing distance via computable Author: Qingyi Zhan, Yuhong Li. Based on the conference/workshop on Continuum Theory and Dynamical Systems held in Lafayette, Louisiana, this reference illustrates the current expansion of knowledge on the relationship between these subjects. It presents new problems in hyperspaces, induced maps, universal maps, fixed-point sets.

Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions. [AbrahamMarsden87] R. Abraham and J. E. Marsden, Foundations of Mechanics, Reading, Mass.: Benjamin/Cummings Publishing Co. Inc. Advanced Book Program, Cited by:

ISBN Kathleen Alligood, Tim Sauer and James Yorke's Chaos is a well-written book that provides a detailed introduction to dynamical systems theory, with a strong emphasis on dissipative systems and low-dimensional chaotic dynamics. [1] D. Anosov, On a certain class of invariant sets of smooth dynamical systems (in Russian), Analytical Methods of the Theory of Nonlinear Oscillations (Kiev ), Akademie der Wissenschaften der Ukrainischen SSR, Kiev (), 39–

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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. 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.

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 Shadowing in Dynamical Systems book : Springer-Verlag Berlin Heidelberg.

Shadowing in Dynamical Systems: Theory and Applications (Mathematics and Its Applications Book ) - Kindle edition by Palmer, K.J. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Shadowing in Dynamical Systems: Theory and Applications (Mathematics and Its Applications Book ).Cited by: 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. 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 by: 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 Price: $ This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones.

It shows the importance of shadowing theory for. The shadowing property and chain mixing are two of the most important concepts in discrete dynamical systems [1], which are closely related to stability and chaotic behavior of dynamical systems. Note: If you're looking for a free download links of Shadowing in Dynamical Systems: Theory and Applications (Mathematics and Its Applications) Pdf, epub, docx and torrent then this site is not for you.

only do ebook promotions online and we does not. The shadowing theory of dynamical systems is now an important and rapidly developing branch of the mordern theory of dynamical systems.

Various types of shadowing properties have been introduced in the literature since Anosov and Bowen's works, and, nowadays, these notions are intensively studied by many authors in the platform of topological. Three main aspects of shadowing in discrete dynamical systems are addressed. First, a new proof of the classical infinite-time shadowing theorem for hyperbolic diffeomorphisms is given.

Shadowing in dynamical systems Item Preview remove-circle Shadowing for Flows -- Ch. Topologically Stable, Structurally Stable, and Generic Systems -- Shadowing and Topological Stability -- Shadowing in Structurally Stable Systems -- The Case of a Flow -- Borrow this book to access EPUB and PDF files.

IN Pages: The lesson of a mathematical theorem known as the shadowing lemma is that, at least for a certain class of dynamical systems and possibly for all chaotic systems, it is impossible to determine who is right, a believer in free will or a believer in deterministic, materialistic laws.

A Shadowing lemma is also a fictional creature in the Discworld. See Shadowing lemma. In the theory of dynamical systems, the shadowing lemma is a lemma describing the behaviour of pseudo-orbits near a hyperbolic invariant ally, the theory states that every pseudo-orbit (which one can think of as a numerically computed trajectory with rounding errors on every step) stays uniformly.

Surveillance, following someones movements. All pages with titles beginning with Shadowing. All pages with titles containing Shadowing.

Shadow (disambiguation) The shadowing lemma, a key result in the theory of dynamical systems. #N#Disambiguation page providing links to topics that could be referred to by the same search term.

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 in Dynamical Systems Theory and Applications MATHEMATICS AND ITS APPLICATIONS Volume 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. We recall that, if S ∈ C 0 (X, X), the family S n, n ∈ N, is called a discrete dynamical system or discrete semigroup.

If S is a C 0-diffeomorphism from X to X, then the family S m, m ∈ Z, forms a discrete group. Most of the properties described below are also valid for discrete dynamical systems.

TY - CHAP. T1 - Shadowing in Chaotic Systems. AU - Poon, L. AU - Dawson, S P. AU - Grebogi, Celso. AU - Sauer, T. AU - Yorke, J.

PY - Y1 - Cited by: 1. This book is a comprehensive overview of modern dynamical systems that covers the major areas. The authors begin with an overview of the main areas of dynamics: ergodic theory, where the emphasis is on measure and information theory; topological dynamics, where the phase space is a topological space and the "flows" are continuous transformations on these spaces; differentiable Pages: This book is a comprehensive overview of modern dynamical systems that covers the major areas.

The authors begin with an overview of the main areas of dynamics: ergodic theory, where the emphasis is on measure and information theory; topological dynamics, where the phase space is a topological space and the "flows" are continuous transformations on these spaces; differentiable dynamics where /5(6).This section contains basic definitions and some results needed in the sequel concerning the shadowing property and the inverse shadowing property.

We refer to the Pilyugin's book and the survey paper for more details on the subject and the theory of dynamical by: 7.