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SURVEY Towards a global view of dynamical systems, for the C1-topology

Published online by Cambridge University Press:  31 May 2011

C. BONATTI
C. BONATTI*
Affiliation:
Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS, Université de Bourgogne, Dijon 21004, France (email: bonatti@u-bourgogne.fr)
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Abstract

This paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits Diff1(M) into disjoint C1-open regions whose union is C1-dense, and conjectures state that each of these open sets and their complements is characterized by the presence of:

  • • either a robust local phenomenon;

  • • or a global structure forbidding this local phenomenon.

Other conjectures state that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 4 , August 2011 , pp. 959 - 993
Copyright
Copyright © Cambridge University Press 2011

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