Rigorous mathematical treatment of holomorphic dynamical systems in one and several variables - properties of Julia and Mandelbrot sets, thermodynamic formalism.
Rigorous mathematical treatment of dissipative dynamical systems such as the Henon map and the Lorenz equation - strange attractors, nonuniform hyperbolicity and decay of correlation.
Rigorous mathematical treatment of conservative dynamical systems like the standard map, Hamiltonian systems and quasi-periodic Schrödinger operators - invariant tori, nonuniform hyperbolicity and diffusion.
The project has a co-operation with IMPA (Rio de Janeiro), financed by STINT, and it participates in a co-operation with Yale and in one ESF-network. For more information, see www.math.kth.se/math br>esearch/dynsyst/.
Ergodic theory, KAM theory, Dynamic systems