Modern theory of dynamical systems
- To show the current state of research in the field of dynamic systems, the beginning of which dates back to the classical works of A. Poincare, A. M. Lyapunov, A. A. Andronov and his school of nonlinear oscillations, which determined many achievements of specialists in the direction of studying the stability and theory of bifurcations of dynamic systems for many years to come.
- To explain the phenomenon of "hyperbolic revolution", begun in the works of D. V. Anosov and S. Smale, and the associated cascade of works in the field of topological classification of dynamic systems on manifolds with complex dynamics.
- To give an idea of the methods of the qualitative theory of dynamic systems, closely related to the study of the topology of the phase spaces on which they are defined.
- Know calssification theorem for cascades on surfaces
- understanding of dynamics on the circle
- Understanding of the interrelation between dynamics and topology of ambient manifold. T
- Understanding resuluts on topological structure of multidimensional manifolds (dimensions greater than three) that admit Morse-Smale flows and cascades without heteroclinic intersections of saddle periodic points with Morse index 1 or n-1.
- Theme 1. Dynamics of one-dimensional mappings.
- Theme 2. Classification of flows, foliations and cascades on surfaces with regular and chaotic dynamics.
- Theme 3. The topology of three-dimensional manifolds and a description of structurally stable flows and cascades, the dynamic properties of which are most closely related to the topological characteristics of the carrier phase space.
- Theme 4. Topological structure of multidimensional manifolds (dimensions greater than three) that admit Morse-Smale flows and cascades without heteroclinic intersections of saddle periodic points with Morse index 1 or n-1.
- Grines V., Medvedev Timur, Pochinka O. Dynamical Systems on 2- and 3-Manifolds. Switzerland : Springer, 2016.
- Shilnikov L.P., Shilnikov A.L., Turaev D.V., Chua L.O. Methods Of Qualitative Theory In Nonlinear Dynamics (Part II). World Sci //Singapore, New Jersey, London, Hong Kong. – 2001.
- Dynamical Systems on 2- and 3-Manifolds, XXVI, 295 p., Grines, V. Z., Medvedev, T. V., Pochinka, O. V., 2016