Dynamics of Hénon-like maps

Hénon maps are among the most studied dynamical systems. Hénon-like maps are invertible holomorphic maps, defined on some convex bounded domain of $\mathbb C^k$, that have an expanding behaviour in $p$ directions and contracting behaviour in the remaining $k-p$ directions. They form a large class of dynamical systems in any dimension, that contain Hénon maps in dimension 2. In this talk, we show that the sequence of their dynamical degrees is non-decreasing until the main dynamical degree, and non-increasing after that. As an application, we also show that their Green currents are woven. This is a joint work with Fabrizio Bianchi and Tien-Cuong Dinh.