Dynamics and geometry in low dimensions

Abstract

This project is a continuation of two previous thematic projects supported by FAPESP with numbers 2006/03829-2 and 2011/16265-8. The present group includes researchers working on dynamical systems and low-dimensional geometry and has senior as well as and young researchers, including recent hires. The areas covered by the project are: dynamics in dimension 2: dynamics of homeomorphisms and diffeomorphisms of the torus; topological dynamics on surfaces; Hénon maps; Teichmüller Theory and its connections with dynamics and geometry in low dimensions; endomorphisms of the interval, critical circle maps, renormalization and parameter space; hamiltonian dynamics; pseudo-holomorphic curves and symplectic dynamics; complex dynamics in dimensions 1 and 2; continuous and differentiable ergodic theory of finite and infinite measures; thermodynamic formalism and ergodic optimization. The purpose of this proposal is to continue to the work we have been doing and also aims to expand the activities of the group that has grown and includes new researchers and new areas of research.