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Dynamics, Geometry and Groups Seminar

Speaker: Lingfeng Lu (³ÉÈË´óƬ)

Title: Periodic orbits and transitivity of Anosov flows on (non-compact) 3-manifolds

Abstract:
A dynamical system is said to be transitive if it has an orbit that is dense in the ambient space. For hyperbolic dynamical systems, and in particular for Anosov flows, transitivity is closely connected to their periodic orbits. In this talk, we will first recall some classical results on this relationship for Anosov flows on compact 3-manifolds. Then together with the help of some more recent approaches, we will discuss a construction of transitive Anosov flows on non-compact regular covers of the ambient manifolds. If time permits, we will also discuss a criterion for transitivity on any regular abelian cover. This is joint work with Thomas Barthelmé.