Seminar on Topological Dynamics

The central object of study in topological dynamics is a topological dynamical system, i.e. a topological space, together with a continuous transformation, a continuous flow, or more generally, a semigroup of continuous transformations of that space. The origins of topological dynamics lie in the study of asymptotical properties of trajectories of systems of autonomous ordinary differential equations, in particular, the behavior of limit sets and various manifestations of "repetitiveness" of the motion, such as periodic trajectories, recurrence and minimality, stability, non-wandering points. The pionering work of Herny Ponicaré on the study of the topological properties of solutions of differential equations and the great impetus given by George Birkhoff in his celebrated monography on Dynamical Systems are considered by many researches as the origins of this field.