The research in our group centers on several aspects of Dynamical Systems. The modern theory of dynamical systems started with the work of Poincaré and, since then, grew into a mature and very active branch of mathematical research. The main goal of this project is to further the study of the following areas of dynamical systems theory:
Hamiltonian systems with two degrees of freedom, their dynamical and topological aspects.
Two-dimensional homeomorphisms and diffeomorphisms such as Hénon maps and twits maps of the annulus.
Renormalization theory in dimensions 1 and 2.
Interval endomorphisms (e.g., delicate analytic questions such as decay of geometry and existence of invariant measures).
Critical circle mappings: renormalization and parameter space.
Teichmueller theory and connections with low dimensional dynamics.
Differentiable and continuous ergodic theory of finite and infinite measures.
While dynamical systems theory developed it also moved
away from other branchs of mathematics which were also
started by Poincaré: symplectic geometry and
topology. Another important goal of this project is to
look for and to develop connections between these areas to
the point of making it possible to use techniques of each
area to attack problems of the other.