Geometry, Topology and Dynamics Seminar
Amie Wilkinson
Northwestern University
Centralizers of C^1 generic diffeomorphisms
Abstract: The *centralizer* C(f) of a diffeomorphism f is the set of all diffeomorphisms that commute with f. C(f) is
naturally viewed as the group of symmetries of f; for example, if f embeds in a flow, then C(f) contains
that flow, which is isomorphic to the real numbers. We say that f has *trivial centralizer* if C(f) is precisely
the group generated by f; that is, f commutes only with its iterates f^n, n in Z. Smale has asked whether
any diffeomorphism can be approximated by one with trivial centralizer.
In this talk I will discuss some answers to this and related questions, in the C^1 topology on
diffeomorphisms. This is joint work with Sylvain Crovisier and Christian Bonatti.
Monday November 28, 2005 at 3:00 PM in SEO 512