Hyperbolic Dynamical Systems

Hasselblatt, Boris

doi:10.1016/b0-12-512666-2/00407-7

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Hyperbolic and Parabolic Paradigms1

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2014

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Cited by 11 publications

(1 citation statement)

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“…This kind of behavior appears in systems with hyperbolic and partially hyperbolic behavior [8,Section 6], [7,1,9]. Example 2.1 in the case when the group G is a torus T n provides simple particular cases for both hyperbolic and partially hyperbolic situations.…”

Section: Hyperbolic and Parabolic Paradigmsmentioning

confidence: 99%

Spectral Properties and Combinatorial Constructions in Ergodic Theory

Katok¹,

Thouvenot²

2006

Handbook of Dynamical Systems

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Section: Hyperbolic and Parabolic Paradigmsmentioning

confidence: 99%

Spectral Properties and Combinatorial Constructions in Ergodic Theory

Katok¹,

Thouvenot²

2006

Handbook of Dynamical Systems

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Spatial structure of Sinai–Ruelle–Bowen measures

Chernov

Korepanov

2014

Physica D: Nonlinear Phenomena

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Nonexistence of Bonatti–Langevin examples of Anosov flows on closed four manifolds

Carballo

Morales

Martín

2007

Topology and its Applications

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Bonatti and Langevin constructed an Anosov flow on a closed 3-manifold with a transverse torus intersecting all orbits except one [C. Bonatti, R. Langevin, Un exemple de flot d'Anosov transitif transverse à un tore et non conjugué à une suspension, Ergodic Theory Dynam. Systems 14 (4) (1994), 633-643]. We shall prove that these flows cannot be constructed on closed 4-manifolds. More precisely, there are no Anosov flows on closed 4-manifolds with a closed, incompressible, transverse submanifold intersecting all orbits except finitely many closed ones. The proof relies on the analysis of the trace of the weak invariant foliations of the flow on the transverse submanifold.

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Hyperbolic Dynamical Systems

Cited by 11 publications

References 92 publications

Spectral Properties and Combinatorial Constructions in Ergodic Theory

Spectral Properties and Combinatorial Constructions in Ergodic Theory

Spatial structure of Sinai–Ruelle–Bowen measures

Nonexistence of Bonatti–Langevin examples of Anosov flows on closed four manifolds

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