Integrability and linearization of dynamical systems
The proposed research includes the following  two  main directions:
(1) Using methods and tools of algebraic geometry and computational  algebra, we study the integrability of the nonlinear dynamical  systems. We focus on finding the varieties of integrability of dynamical systems with the emphasize on the higher dimensional systems. Our approaches are based on combining symbolic computations with methods of  the theory of  integrability of dynamical systems.  We then study  bifurcations of limit cycles and critical periods arising after perturbations of   higher dimensional integrable systems of  differential equation. Furthermore, we intend to study the problem of isochronicity (which is equivalent to the problem of linearization).  
(2) We propose to study the global topological linearization, linearization of integral manifold, smooth linearization   with the emphasis  on the study of the linearization of non-autonomous systems when the nonlinear term is unbounded or linear system does not possess exponential dichotomy (in critical state). Up to now there are few results concerning the linearization