Invariant submanifolds for conformal dynamics

In a work with Jacques Fejoz, we consider the conformal dynamics on a symplectic manifold , i.e. for which the symplectic form is transformed colinearly to itself. In the non-symplectic case, we study the problem of isotropy and uniqueness of invariant submanifolds. More precisely, in this talk, I will explain a relation between topological entropy and isotropy and some uniqueness results.