Appears in collection : 2024 - T2 - WS2 - Group actions with hyperbolicity and measure rigidity

Let $\mathrm{X}$ be a K3 surface with a large automorphism group $\mathrm{Aut}(\mathrm{X})$ (we do not assume that it contains any parabolic elements). Consider a probability measure $\mu$ on $\mathrm{Aut}(\mathrm{X})$ using the work of Cantat and DuJardin (2020) we study hyperbolic, ergodic -stationary probability measures, and the supports of their conditional measures on the stable and unstable manifolds (which are a.e. biholomorphic to ) using the techniques of Benoist and Quint (2011), and Eskin and Mirzakhani (2018).