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

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) in disjoint C1-open regions whose union is C1-dense, and conjectures state that these open set, and their complement, are characterized by the presence of • either a robust local phenomenon • or a global structure forbiding this local phenomenon. Other conjectures states 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.
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https://hal.archives-ouvertes.fr/hal-00463421
Contributor : Christian Bonatti <>
Submitted on : Friday, March 26, 2010 - 12:43:00 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Wednesday, November 30, 2016 - 3:36:52 PM

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Christian Bonatti. Towards a global view of dynamical systems, for the C1-topology.. 2010. ⟨hal-00463421⟩

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