Marcelo Alves: Legendrian contact homology and topological entropy

The topological entropy is a dynamical invariant which codifies in a single non-negative number the complexity of a dynamical system.

In this talk I will explain how one can use Legendrian contact homology to obtain positive lower bounds for the topological entropy of Reeb flows on contact 3-manifolds. As an application one can establish existence of large families of contact 3-manifolds on which every Reeb flow has positive topological entropy.

If time allows I will explain how similar techniques can be used to prove "forcing of entropy" results for certain Reeb flows in \(S^3 \)and \(T^3\).