A major part of dynamical system theory studies the iteration of diffeomorphisms under various assumptions, geometric or analytic or otherwise. It is also interesting to study them collectively. In particular, , the set of diffeomorphisms of some manifold and some number , is a group. It is for instance of interest to know when it [...]
Posts Tagged ‘genericity’
T. Fisher: Diffeomorphisms with Trivial Centralizers
Posted in Dynamics, talks, tagged centralizers, genericity, group actions, hyperbolicity, smooth dynamics, smoothness on June 3, 2010 | Leave a Comment »
Alpern genericity theorem
Posted in Dynamics, papers, tagged Dynamics, ergodic theory, genericity, topological dynamics on January 27, 2010 | Leave a Comment »
Frédéric Le Roux has written a very lucid exposition of the Alpern genericity theorem. This theorem states that the same ergodic properties are generic in the set of volume-preserving measurable transformations and in the set of volume-preserving homeomorphisms. More precisely, endow with the weak topology, i.e., the coarsest generated by , for all measurable [...]
Finite codimension in Banach spaces
Posted in Dynamics, Meetings, talks, tagged Aubry-Mather theory, codimension, genericity, prevalence on November 27, 2009 | Leave a Comment »
On 2009/11/27 at IHP on the occasion of the Katok 65 conference, Patrick BERNARD presented his notion of codimension in Banach spaces with applications to Mather measures and the transversality theorem. B will denote the ambient Banach space. A large part of the theory extends to Fréchet spaces (things get tougher once C^1 smoothness is [...]
