6533b82ffe1ef96bd1295d21

RESEARCH PRODUCT

Centralizers of C^1-generic diffeomorphisms

Christian Bonatti Sylvain Crovisier Amie Wilkinson

subject

Mathematics::Dynamical Systems[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]FOS: Mathematics[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)Mathematics - Dynamical SystemsMathematics::Symplectic Geometry

description

On the one hand, we prove that the spaces of C^1 symplectomorphisms and of C^1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On the other hand, we show that the space of C^1 diffeomorphisms of the circle and a non-empty open set of C^1 diffeomorphisms of the two-sphere contain dense subsets of diffeomorphisms whose centralizer has a sub-group isomorphic to R.

yearjournalcountryeditionlanguage
2006-10-02
http://arxiv.org/abs/math/0610064