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.

Twodimensional
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.

Ergodic optimization.

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.
Cuurent Thematic Grant:
Projeto
FAPESP
16/250538