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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Ordinary Differential Equations and Dynamical Systems


Real and complex one-dimensional dynamics, geometry of fractal sets, multidimensional complex dynamics, theory of singularities of vector fields and distributions and related topics in real analytic geometry.



  • Complex dynamics, geometry of fractal sets
  • Differential geometry, polynomial vector fields, generalized Abelian integrals and limit cycles in higher dimensional differential systems
  • Affine algebraic geometry (classification of complex plane algebraic curves, application to the problem of limit cycles of polynomial vector fields)
  • Ordinary differential equations: Fuchsian linear differential equations and nonlinear equations (Painleve equations), special functions (hypergeometric function, Heun's function and others)
  • Finite and infinite-dimensional gradient flows, singularities of analytic vector fields; elliptic and parabolic nonlinear partial differential equations and systems; calculus of variations on metric measure spaces
  • Ergodic theory of smooth dynamical systems
  • Singularities of Pfaff systems and distributions, geometric control theory; contact geometry
  • Complex and real analytic sets, singularities of sets and analytic functions, applications to differential equations
  • One dimensional real dynamics
  • Dynamical systems, stochastic games
  • Holomophic dynamics, geometry of fractal sets
  • Holomorphic dynamics, ergodic theory of smooth dynamical systems
  • Differential equations: polynomial vector fields, normal forms of singularities, holomorphic foliations