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Hyperbolic sets that are not locally maximal
 Ergod. Th. Dynamic. Systems
, 2006
"... This papers addresses the following topics relating to the structure of hyperbolic sets: First, hyperbolic sets that are not contained in locally maximal hyperbolic sets. Second, the existence of a Markov partition for a hyperbolic set. We construct new examples of hyperbolic sets which are not cont ..."
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Cited by 3 (3 self)
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This papers addresses the following topics relating to the structure of hyperbolic sets: First, hyperbolic sets that are not contained in locally maximal hyperbolic sets. Second, the existence of a Markov partition for a hyperbolic set. We construct new examples of hyperbolic sets which
MARKOV PARTITIONS FOR HYPERBOLIC SETS
"... Abstract. We show that if f is a diffeomorphism of a manifold to itself, Λ is a mixing (or transitive) hyperbolic set, and V is a neighborhood of Λ, then there exists a mixing (or transitive) hyperbolic set Λ ̃ with a Markov partition such that Λ ⊂ Λ ̃ ⊂ V. Furthermore, we show that in the topologi ..."
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Abstract. We show that if f is a diffeomorphism of a manifold to itself, Λ is a mixing (or transitive) hyperbolic set, and V is a neighborhood of Λ, then there exists a mixing (or transitive) hyperbolic set Λ ̃ with a Markov partition such that Λ ⊂ Λ ̃ ⊂ V. Furthermore, we show
ON THE INTERSECTION OF SECTIONALHYPERBOLIC SETS
"... Abstract. We analyse the intersection of positively and negatively sectionalhyperbolic sets for flows on compact manifolds. First we prove that such an intersection is hyperbolic if the intersecting sets are both transitive (this is false without such a hypothesis). Next we prove that, in general, ..."
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Abstract. We analyse the intersection of positively and negatively sectionalhyperbolic sets for flows on compact manifolds. First we prove that such an intersection is hyperbolic if the intersecting sets are both transitive (this is false without such a hypothesis). Next we prove that, in general
TRANSITIVE HYPERBOLIC SETS ON SURFACES
"... Abstract. We show that every transitive hyperbolic set on a surface is included in a locally maximal hyperbolic set. 1. History The history of hyperbolic dynamics can be traced back to two related directions of research: First, the study of geodesic flows such as the work of Hadamard, Hedlund, and ..."
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Abstract. We show that every transitive hyperbolic set on a surface is included in a locally maximal hyperbolic set. 1. History The history of hyperbolic dynamics can be traced back to two related directions of research: First, the study of geodesic flows such as the work of Hadamard, Hedlund
ON THE VOLUME OF SINGULARHYPERBOLIC SETS
, 2005
"... Abstract. An attractor Λ for a 3vector field X is singularhyperbolic if all its singularities are hyperbolic and it is partially hyperbolic with volume expanding central direction. We prove that C 1+α singularhyperbolic attractors, for some α> 0, always have zero volume, thus extending an analo ..."
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Cited by 8 (4 self)
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Abstract. An attractor Λ for a 3vector field X is singularhyperbolic if all its singularities are hyperbolic and it is partially hyperbolic with volume expanding central direction. We prove that C 1+α singularhyperbolic attractors, for some α> 0, always have zero volume, thus extending
Hyperbolic Sets for Noninvertible Maps and Relations
, 1996
"... This thesis presents a theory of hyperbolic structures and dynamics of smooth noninvertible maps and relations. In this context, it includes a new proof of the stable manifold theorem for fixed points, the shadowing lemma, and a version of the stable manifold theorem for hyperbolic sets. It also g ..."
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Cited by 6 (2 self)
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This thesis presents a theory of hyperbolic structures and dynamics of smooth noninvertible maps and relations. In this context, it includes a new proof of the stable manifold theorem for fixed points, the shadowing lemma, and a version of the stable manifold theorem for hyperbolic sets. It also
Topological structure of (partially) hyperbolic sets with positive volume
, 2006
"... Abstract. We consider both hyperbolic sets and partially hyperbolic sets attracting a set of points with positive volume in a Riemannian manifold. We obtain several results on the topological structure of such sets for diffeomorphisms whose differentiability is bigger than one. We show in particular ..."
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Cited by 6 (3 self)
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Abstract. We consider both hyperbolic sets and partially hyperbolic sets attracting a set of points with positive volume in a Riemannian manifold. We obtain several results on the topological structure of such sets for diffeomorphisms whose differentiability is bigger than one. We show
Hyperbolic sets with nonempty interior, Discrete Contin
 Dyn. Syst
"... Abstract. In this paper we study hyperbolic sets with nonempty interior. We prove the folklore theorem that every transitive hyperbolic set with interior is Anosov. We also show that on a compact surface every locally maximal hyperbolic set with nonempty interior is Anosov. Finally, we give example ..."
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Cited by 4 (1 self)
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Abstract. In this paper we study hyperbolic sets with nonempty interior. We prove the folklore theorem that every transitive hyperbolic set with interior is Anosov. We also show that on a compact surface every locally maximal hyperbolic set with nonempty interior is Anosov. Finally, we give
Flows on vector bundles and hyperbolic sets
 Trans. AMS
, 1988
"... Abstract. This note deals with C. Conley's topological approach to hyperbolic invariant sets for continuous flows. It is based on the notions of isolated invariant sets and Morse decompositions and it leads to the concept of weak hyperbolicity. 1. Introduction. It is our aim to give an expositi ..."
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Cited by 8 (0 self)
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Abstract. This note deals with C. Conley's topological approach to hyperbolic invariant sets for continuous flows. It is based on the notions of isolated invariant sets and Morse decompositions and it leads to the concept of weak hyperbolicity. 1. Introduction. It is our aim to give
Geometric measures for hyperbolic sets on surfaces
 In preparation
"... Abstract. We present a moduli space for all hyperbolic basic sets of diffeomorphisms on surfaces that have an invariant measure that is absolutely continuous with respect to Hausdorff measure. To do this we introduce two new invariants: the measure solenoid function and the cocyclegap pair. We exte ..."
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Cited by 1 (1 self)
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Abstract. We present a moduli space for all hyperbolic basic sets of diffeomorphisms on surfaces that have an invariant measure that is absolutely continuous with respect to Hausdorff measure. To do this we introduce two new invariants: the measure solenoid function and the cocyclegap pair. We
Results 1  10
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2,258