Hardcover ISBN:  9780821803691 
Product Code:  MMONO/153 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445683 
Product Code:  MMONO/153.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821803691 
eBook: ISBN:  9781470445683 
Product Code:  MMONO/153.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
Hardcover ISBN:  9780821803691 
Product Code:  MMONO/153 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445683 
Product Code:  MMONO/153.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821803691 
eBook ISBN:  9781470445683 
Product Code:  MMONO/153.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 153; 1996; 325 ppMSC: 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.
ReadershipGraduate 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.

Table of Contents

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 wellwritten 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 twodimensional 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


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Reviews
 Requests
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 wellwritten 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 twodimensional 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