Attractors under autonomous and non-autonomous 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 ; no. 246.

Mathematical surveys and monographs, 0076-5376 ; volume 246

Language:

English

Subjects (All):

Attractors (Mathematics).

Perturbation (Mathematics).

Physical Description:

ix, 246 pages : illustrations ; 27 cm.

Place of Publication:

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

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.

Contents:

Semigroups and global attractors

Upper and lower semicontinuity

Topological structural stability of attractors

Neighborhood of a critical element

Morse-Smale semigroups

Non-autonomous dynamical systems and their attractors

Topological structural stability

Neighborhood of a global hyperbolic solution

Non-autonomous Morse-Smale dynamical systems.

Notes:

Includes bibliographical references (pages 231-241) and index.

ISBN:

9781470453084

1470453088

OCLC:

1145589238