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Attractors Under Autonomous and Non-autonomous Perturbations

Matheus C. Bortolan Universidade Federal de Santa Catarina, Florianópolis SC, Brazil
Alexandre N. Carvalho Universidade de São Paulo, São Carlos SP, Brazil
José A. Langa Universidad de Sevilla, Seville, Spain
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Hardcover ISBN: 978-1-4704-5308-4
Product Code: SURV/246
List Price: $140.00 MAA Member Price:$126.00
AMS Member Price: $112.00 Electronic ISBN: 978-1-4704-5684-9 Product Code: SURV/246.E List Price:$140.00
MAA Member Price: $126.00 AMS Member Price:$112.00
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List Price: $210.00 MAA Member Price:$189.00
AMS Member Price: $168.00 Click above image for expanded view Attractors Under Autonomous and Non-autonomous Perturbations Matheus C. Bortolan Universidade Federal de Santa Catarina, Florianópolis SC, Brazil Alexandre N. Carvalho Universidade de São Paulo, São Carlos SP, Brazil José A. Langa Universidad de Sevilla, Seville, Spain Available Formats:  Hardcover ISBN: 978-1-4704-5308-4 Product Code: SURV/246  List Price:$140.00 MAA Member Price: $126.00 AMS Member Price:$112.00
 Electronic ISBN: 978-1-4704-5684-9 Product Code: SURV/246.E
 List Price: $140.00 MAA Member Price:$126.00 AMS Member Price: $112.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$210.00 MAA Member Price: $189.00 AMS Member Price:$168.00
• Book Details

Mathematical Surveys and Monographs
Volume: 2462020; 246 pp
MSC: Primary 34; 35; Secondary 37;

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.

Graduate students and researchers interested in dynamical systems.

• Chapters
• Introduction
• 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

• Reviews

• The figures included in the book, which are many, are informative and helpful for the discussion. The notes in each chapter provide good maps to the extensive references, including historical commentary on the literature.

Justin T. Webster, University of Maryland, Baltimore County
• Request Review Copy
• Get Permissions
Volume: 2462020; 246 pp
MSC: Primary 34; 35; Secondary 37;

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.

Graduate students and researchers interested in dynamical systems.

• Chapters
• Introduction
• 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
• The figures included in the book, which are many, are informative and helpful for the discussion. The notes in each chapter provide good maps to the extensive references, including historical commentary on the literature.

Justin T. Webster, University of Maryland, Baltimore County
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