3 papers
math.DS2025
Measure Rigidity beyond Homogeneous Dynamics
Simion Filip
We describe recent work that extends some of the measure and topological rigidity results in dynamical systems from situations homogeneous under a Lie group to quite general manifo…
math.DG2025
Finiteness of totally geodesic hypersurfaces
Simion Filip, David Fisher, Ben Lowe
We prove that a closed negatively curved analytic Riemannian manifold that contains infinitely many totally geodesic hypersurfaces is isometric to an arithmetic hyperbolic manifold…
math.DS2025
Measure rigidity for generalized u-Gibbs states and stationary measures via the factorization method
Aaron Brown, Alex Eskin, Simion Filip +1
We obtain measure rigidity results for stationary measures of random walks generated by diffeomorphisms, and for actions of on smooth manifolds. O…