Robust transitivity implies almost robust ergodicity

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64492In this paper we show the relation between robust transitivity and robust ergodicity for conservative diffeomorphisms. In dimension 2 robustly transitive systems are robustly ergodic. For the three dimensional case, we define it almost robust ergodicity and prove that generically robustly transitive systems are almost robustly ergodic, if the Lyapunov exponents are nonzero. We also show in higher dimensions, that under some conditions robust transitivity implies robust ergodicity.12 pagesDynamical Systems37Axx, 37CxxRobust transitivity implies almost robust ergodicitytext