Colloquium: Tuesday, March 7, 2 pm. Speaker: Tom Meyerovitch (Ben Gurion). Title: “On the pseudo-orbit tracing property and algebraic actions of countable groups”.
Topological dynamics studies behaviour of orbits under continuous transformations. Algebraic dynamics is the name attached to the study of automorphisms acting on a compact abelian group, from a “dynamical point of view”. In the 1970’s, motivated by the study of Axiom A maps, R. Bowen introduced the pseudo-orbit tracing property for a homeomorphism. Roughly, this property asserts that every sequence of points that is locally a perturbation of an orbit is globally traced by a genuine orbit. The notion of pseudo-orbit tracing property naturally extends to actions of general groups. We will see what makes dynamical systems admitting the pseudo-orbit tracing property interesting, in particular in combination with another fundamental dynamical property called expansiveness, and how all this relates to algebraic dynamical systems.
