Abstract: We discuss the stable ergodicity of the action of groups of diffeomorphisms on smooth manifolds. The existence of such actions is
well-known only on one-dimensional manifolds. As a consequence of a new local and stable mechanism/phenomenon, called quasi-conformal blender, one can overcome this restriction and construct higher-dimensional examples. In particular, every closed manifold admits stably ergodic finitely generated group actions by smooth diffeomorphisms. One can also prove the stable ergodicity of the natural action of a generic pair of matrices near the identity on a sphere of arbitrary dimension. The quasi-conformal blender is developed in the context of pseudo-semigroup actions of locally defined smooth diffeomorphisms and yields stable local ergodicity in several different settings.
This talk is based on a joint work with M. Nassiri and H. Rajabzadeh
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