Introduction to the Qualitative Theory of Dynamical Systems 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.