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Introduction to the Qualitative Theory of Dynamical Systems on Surfaces

Samuel Kh. Aranson , Novgorod, Russia
G. R. Belitsky Ben-Gurion University of the Negev
E. V. Zhuzhoma Nizhnii Novgorod University
Available Formats:
Hardcover ISBN: 978-0-8218-0369-1
Product Code: MMONO/153
325 pp
List Price: $129.00 MAA Member Price:$116.10
AMS Member Price: $103.20 Electronic ISBN: 978-1-4704-4568-3 Product Code: MMONO/153.E 325 pp List Price:$129.00
MAA Member Price: $116.10 AMS Member Price:$103.20
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List Price: $193.50 MAA Member Price:$174.15
AMS Member Price: $154.80 Click above image for expanded view Introduction to the Qualitative Theory of Dynamical Systems on Surfaces Samuel Kh. Aranson , Novgorod, Russia G. R. Belitsky Ben-Gurion University of the Negev E. V. Zhuzhoma Nizhnii Novgorod University Available Formats:  Hardcover ISBN: 978-0-8218-0369-1 Product Code: MMONO/153 325 pp  List Price:$129.00 MAA Member Price: $116.10 AMS Member Price:$103.20
 Electronic ISBN: 978-1-4704-4568-3 Product Code: MMONO/153.E 325 pp
 List Price: $129.00 MAA Member Price:$116.10 AMS Member Price: $103.20 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:$193.50
MAA Member Price: $174.15 AMS Member Price:$154.80
• Book Details

Translations of Mathematical Monographs
Volume: 1531996
MSC: Primary 58; Secondary 34; 57; 54;

This book is an introduction to the qualitative theory of dynamical systems on manifolds of low dimension (on the circle and on surfaces). Along with classical results, it reflects the most significant achievements in this area obtained in recent times by Russian and foreign mathematicians whose work has not yet appeared in the monographic literature. The main stress here is put on global problems in the qualitative theory of flows on surfaces.

Despite the fact that flows on surfaces have the same local structure as flows on the plane, they have many global properties intrinsic to multidimensional systems. This is connected mainly with the existence of nontrivial recurrent trajectories for such flows. The investigation of dynamical systems on surfaces is therefore a natural stage in the transition to multidimensional dynamical systems.

The reader of this book need be familiar only with basic courses in differential equations and smooth manifolds. All the main definitions and concepts required for understanding the contents are given in the text.

The results expounded can be used for investigating mathematical models of mechanical, physical, and other systems (billiards in polygons, the dynamics of a spinning top with nonholonomic constraints, the structure of liquid crystals, etc.).

In our opinion the book should be useful not only to mathematicians in all areas, but also to specialists with a mathematical background who are studying dynamical processes: mechanical engineers, physicists, biologists, and so on.

Graduate students and researchers working in dynamical systems and differential equations, as well as specialists with a mathematical background who are studying dynamical processes: mechanical engineers, physicists, biologists, etc.

• Chapters
• Chapter 1. Dynamical systems on surfaces
• Chapter 2. Structure of limit sets
• Chapter 3. Topological structure of a flow
• Chapter 4. Local structure of dynamical systems
• Chapter 5. Transformations of the circle
• Chapter 6. Classification of flows on surfaces
• Chapter 7. Relation between smoothness properties and topological properties of flows
• Reviews

• These and many other wonders are revealed in this thorough monograph. Lovers of dynamical systems will find this a mine of interesting information.

Bulletin of the London Mathematical Society
• Consists of seven well-written chapters with mathematical rigor, and only prerequisite knowledge of topology and differential equations on the level of undergraduate students is assumed … contains … not only rich material for studying dynamical systems of two-dimensional manifolds, but also a natural background for understanding properties of multidimensional dynamical systems.

Zentralblatt MATH
• Comprehensive … serves as a good reference for flows on surfaces, and would be well suited for a specialized graduate course on these topics … very well written.

Mathematical Reviews
• Request Review Copy
• Get Permissions
Volume: 1531996
MSC: Primary 58; Secondary 34; 57; 54;

This book is an introduction to the qualitative theory of dynamical systems on manifolds of low dimension (on the circle and on surfaces). Along with classical results, it reflects the most significant achievements in this area obtained in recent times by Russian and foreign mathematicians whose work has not yet appeared in the monographic literature. The main stress here is put on global problems in the qualitative theory of flows on surfaces.

Despite the fact that flows on surfaces have the same local structure as flows on the plane, they have many global properties intrinsic to multidimensional systems. This is connected mainly with the existence of nontrivial recurrent trajectories for such flows. The investigation of dynamical systems on surfaces is therefore a natural stage in the transition to multidimensional dynamical systems.

The reader of this book need be familiar only with basic courses in differential equations and smooth manifolds. All the main definitions and concepts required for understanding the contents are given in the text.

The results expounded can be used for investigating mathematical models of mechanical, physical, and other systems (billiards in polygons, the dynamics of a spinning top with nonholonomic constraints, the structure of liquid crystals, etc.).

In our opinion the book should be useful not only to mathematicians in all areas, but also to specialists with a mathematical background who are studying dynamical processes: mechanical engineers, physicists, biologists, and so on.

Graduate students and researchers working in dynamical systems and differential equations, as well as specialists with a mathematical background who are studying dynamical processes: mechanical engineers, physicists, biologists, etc.

• Chapters
• Chapter 1. Dynamical systems on surfaces
• Chapter 2. Structure of limit sets
• Chapter 3. Topological structure of a flow
• Chapter 4. Local structure of dynamical systems
• Chapter 5. Transformations of the circle
• Chapter 6. Classification of flows on surfaces
• Chapter 7. Relation between smoothness properties and topological properties of flows
• These and many other wonders are revealed in this thorough monograph. Lovers of dynamical systems will find this a mine of interesting information.

Bulletin of the London Mathematical Society
• Consists of seven well-written chapters with mathematical rigor, and only prerequisite knowledge of topology and differential equations on the level of undergraduate students is assumed … contains … not only rich material for studying dynamical systems of two-dimensional manifolds, but also a natural background for understanding properties of multidimensional dynamical systems.

Zentralblatt MATH
• Comprehensive … serves as a good reference for flows on surfaces, and would be well suited for a specialized graduate course on these topics … very well written.

Mathematical Reviews
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