
Low Dimensional Flows and
Hamiltonian Systems:

Dynamical and
topological aspects of flows obtained by
restricting Hamiltonian systems with two degrees
of freedom to constant energy levels. Hofer
conjecture. Geodesic flows on the two dimensional
sphere.

Local properties of
equilibrium points of simple mechanical systems
(kinetic energy + potential energy).

Low Dimensional Discrete
Dynamics:

Homeomorphisms and
diffeomorphisms of the annulus, the cylinder and
the torus. Rotation sets and periofics orbits.
Boyland's conjecture.

Twist mappings.
Rupture of invariant curves. Ergodicity of twist
mappings on the torus.

Families of
diffeomorphisms on surfaces. Hénon mappings.
Implications among orbits and quasilinear models
in two dimensions.

Renormalization in one and
two dimensions:

Renormalization of
critical circle mappings and dissipaive mappings
with one discontinuity. Complete families and
circle endomorphisms. Geometry decay in cubic
families. Henon renormalization.

Complex dynamics.
Thompson groups and Teichmüller spaces. Dynamics
of transcendent holomorphic and meromorphic
functions.

Differentiable Ergodic
Theory:

Small scale structure
and nonstationary dynamics.

Infinite measures and
fractal geometry.

Renormalization and Teichmüller flow.

3dimensional geometry and topology and connections
with surface dynamics

Holomorphic dynamics in one and several dimensions.