Attractors under autonomous and nonautonomous perturbations / Matheus C. Bortolan, Alexandre N. Carvalho, José A. Langa.

Format:

Book

Author/Creator:

Bortolan, Matheus C. (Matheus Cheque), 1985- author.

Carvalho, Alexandre Nolasco de, author.

Langa, José A., author.

Series:

Mathematical surveys and monographs ; Volume 246.

Mathematical surveys and monographs ; Volume 246

Language:

English

Subjects (All):

Attractors (Mathematics).

Perturbation (Mathematics).

Physical Description:

1 online resource (259 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2020]

Language Note:

English

Summary:

This book provides a comprehensive study of how attractors behave under perturbations for both autonomous and non-autonomous problems. Furthermore, the forward asymptotics of non-autonomous dynamical systems is presented here for the first time in a unified manner. When modelling real world phenomena imprecisions are unavoidable. On the other hand, it is paramount that mathematical models reflect the modelled phenomenon, in spite of unimportant neglectable influences discounted by simplifications, small errors introduced by empirical laws or measurements, among others. The authors deal with this issue by investigating the permanence of dynamical structures and continuity properties of the attractor. This is done in both the autonomous (time independent) and non-autonomous (time dependent) framework in four distinct levels of approximation: the upper semicontinuity, lower semicontinuity, topological structural stability and geometrical structural stability. This book is aimed at graduate students and researchers interested in dissipative dynamical systems and stability theory, and requires only a basic background in metric spaces, functional analysis and, for the applications, techniques of ordinary and partial differential equations.

Contents:

Semigraoups and global attractions

Upper and lower semicontinuity

Topological structural stability of attractors

Neighborhood of a critical element

Morse-Smale semigraopus

Non-autonomous dynamical systems and their attractors

Topological structural stability

Neighborhood of a global hyperbolic solution

Non-automomous Morse-Smale dynamical systems.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-5684-2

OCLC:

1151186995