Probabilistic and algebraic aspects of smooth dynamical systems
Abstract
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 and their stability in the sense of Lyapunov. - Two-dimensional diffeomorphisms such as Hénon maps and twits maps of the annulus and torus. - 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. - Teichmüller theory and connections with low dimensional dynamics and geometry. - Differentiable and continuous ergodic theory of finite and infinite measures. - Ergodic optimization. (AU)
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