Attractors Under Autonomous and Non-autonomous Perturbations
Seiten
2020
American Mathematical Society (Verlag)
978-1-4704-5308-4 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5308-4 (ISBN)
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.
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.
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.
Matheus C. Bortolan, Universidade Federal de Santa Catarina, Florianopolis SC, Brazil. Alexandre N. Carvalho, Universidade de Sao Paulo, Sao Carlos SP, Brazil. Jose A. Langa, Universidad de Sevilla, Seville, Spain.
Autonomous theory: Semigroups and global attractors
Upper and lower semicontinuity
Topological structural stability of attractors
Neighborhood of a critical element
Morse-Smale semigroups
Non-autonomous theory: Non-autonomous dynamical systems and their attractors
Upper and lower semicontinuity
Topological structural stability
Neighborhood of a global hyperbolic solution
Non-autonomous Morse-Smale dynamical systems
Bibliography
List of figures
Index.
| Erscheinungsdatum | 08.07.2020 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 650 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-5308-8 / 1470453088 |
| ISBN-13 | 978-1-4704-5308-4 / 9781470453084 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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