Limit sets of discrete dynamical systems

ended

The proposed project aims to deepen our knowledge on limit sets which will provide a better understanding of the long term behavior of a discrete dynamical system. We will investigate the topological size and structure of basins of limit sets and study the properties of statistical limit sets and limit sets of backward trajectories. We will search for a criterion allowing to decide whether a given closed invariant set is a limit set of some backward trajectory. The focus will be on the low-dimensional dynamical systems such as interval maps, maps acting on the circle, graphs, dendrites, Cantor space. We will use methods and techniques from topological dynamics and ergodic theory, including combinatorial and symbolic dynamics, shadowing, specification property, invariant measures and generic points.