0000000000300308

AUTHOR

Amie Wilkinson

showing 2 related works from this author

The centralizer of a C1 generic diffeomorphism is trivial

2007

In this announcement, we describe the solution in the C1 topology to a question asked by S. Smale on the genericity of trivial centralizers: the set of diffeomorphisms of a compact connected manifold with trivial centralizer residual in Diff^1 but does not contain an open and dense subset.

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::Geometric TopologyMathematics::Symplectic Geometry
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Transitive partially hyperbolic diffeomorphisms on 3-manifolds

2005

Abstract The known examples of transitive partially hyperbolic diffeomorphisms on 3-manifolds belong to 3 basic classes: perturbations of skew products over an Anosov map of T 2 , perturbations of the time one map of a transitive Anosov flow, and certain derived from Anosov diffeomorphisms of the torus T 3 . In this work we characterize the two first types by a local hypothesis associated to one closed periodic curve.

Discrete mathematicsTransitive relationPure mathematicsMathematics::Dynamical Systems010102 general mathematics05 social sciencesSkewTorus01 natural sciencesMathematics::Geometric TopologyFlow (mathematics)Structural stability0502 economics and businessAnosov diffeomorphismGeometry and Topology0101 mathematicsMathematics::Symplectic Geometry050203 business & managementMathematicsTopology
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