Search results for "Smale diffeomorphisms"

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Topological classification of gradient-like diffeomorphisms on 3-manifolds

2004

Abstract We give a complete invariant, called global scheme , of topological conjugacy classes of gradient-like diffeomorphisms, on compact 3-manifolds. Conversely, we can realize any abstract global scheme by such a diffeomorphism.

Discrete mathematicsPure mathematicsMathematics::Dynamical SystemsTopological classificationTopological classificationGeometry and TopologyDiffeomorphismInvariant (mathematics)Topological conjugacyMathematics::Symplectic GeometryMorse–Smale diffeomorphismsMathematics3-manifoldsTopology
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Conjugate unstable manifolds and their underlying geometrized Markov partitions

2000

Abstract Conjugate unstable manifolds of saturated hyperbolic sets of Smale diffeomorphisms are characterized in terms of the combinatorics of their geometrized Markov partitions. As a consequence, the relationship between the local and the global point of view is also made explicit.

Discrete mathematicsSmale diffeomorphismsMathematics::Dynamical SystemsMarkov chainInvariant manifoldsGeometrized Markov partitionsPoint (geometry)Geometry and TopologyMathematics::Symplectic GeometryMathematics::Geometric TopologyConjugateMathematicsTopology and its Applications
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