Hyperbolic Sets, Shadowing and Persistence for Noninvertible Mappings in Banach Spaces
Hyperbolic Sets, Shadowing and Persistence for Noninvertible Mappings in Banach Spaces

Author: Bernard Lani-Wayda

Publisher: CRC Press

Published: 2022-09-16

Total Pages: 153

ISBN-13: 100071683X

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This text gives a self-contained and detailed treatment of presently known results, and new theorems on hyperbolicity, shadowing, complicated motion, and robustness. The book is intended to provide a dependable reference for researchers wishing to apply such results. This book will be of particular interest to researchers and students interested in dynamical systems, particularly in noninvertible maps and infinite dimensional semi-flows or maps and global analysis.

Shadowing in Dynamical Systems
Shadowing in Dynamical Systems

Author: K.J. Palmer

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 307

ISBN-13: 1475732104

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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.

Solution Sets of Differential Equations in Abstract Spaces
Solution Sets of Differential Equations in Abstract Spaces

Author: Robert Dragoni

Publisher: CRC Press

Published: 1996-04-03

Total Pages: 42

ISBN-13: 9780582294509

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This book presents results on the geometric/topological structure of the solution set S of an initial-value problem x(t) = f(t, x(t)), x(0) =xo, when f is a continuous function with values in an infinite-dimensional space. A comprehensive survey of existence results and the properties of S, e.g. when S is a connected set, a retract, an acyclic set, is presented. The authors also survey results onthe properties of S for initial-value problems involving differential inclusions, and for boundary-value problems. This book will be of particular interest to researchers in ordinary and partial differential equations and some workers in control theory.

Inner Product Spaces and Applications
Inner Product Spaces and Applications

Author: T M Rassias

Publisher: CRC Press

Published: 1997-10-08

Total Pages: 284

ISBN-13: 9780582317116

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In this volume, the contributing authors deal primarily with the interaction among problems of analysis and geometry in the context of inner product spaces. They present new and old characterizations of inner product spaces among normed linear spaces and the use of such spaces in various research problems of pure and applied mathematics. The methods employed are accessible to students familiar with normed linear spaces. Some of the theorems presented are at the same time simple and challenging.

The Theory of Quantaloids
The Theory of Quantaloids

Author: K I Rosenthal

Publisher: CRC Press

Published: 2014-07-22

Total Pages: 160

ISBN-13: 1498710409

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This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales. The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories.

Integral Expansions Related to Mehler-Fock Type Transforms
Integral Expansions Related to Mehler-Fock Type Transforms

Author: B N Mandal

Publisher: CRC Press

Published: 2020-11-25

Total Pages: 144

ISBN-13: 1000115224

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An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.

Backward Stochastic Differential Equations
Backward Stochastic Differential Equations

Author: N El Karoui

Publisher: CRC Press

Published: 1997-01-17

Total Pages: 236

ISBN-13: 9780582307339

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This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.

Progress in Elliptic and Parabolic Partial Differential Equations
Progress in Elliptic and Parabolic Partial Differential Equations

Author: A Alvino

Publisher: CRC Press

Published: 1996-05-15

Total Pages: 236

ISBN-13: 9780582259706

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This Research Note collects reports of the invited plenary addresses given during the conference Elliptic and Parabolic Partial Differential Equations and Applications held in Capri, Italy, 19-23 September 1994. The conference was devoted to new developments in partial differential equations of elliptic and parabolic type and to their applications in various fields.