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Leafwise quasigeodesic foliations in dimension three and the funnel property

Part of: Smooth dynamical systems: general theory Global differential geometry Differential topology Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  31 August 2022

ANINDYA CHANDA Open the ORCID record for ANINDYA CHANDA [Opens in a new window]  and
SÉRGIO R. FENLEY Open the ORCID record for SÉRGIO R. FENLEY [Opens in a new window]
ANINDYA CHANDA
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA (e-mail: ac17t@fsu.edu, achanda@math.fsu.edu)
SÉRGIO R. FENLEY*
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA (e-mail: ac17t@fsu.edu, achanda@math.fsu.edu)
*
e-mail: fenley@math.fsu.edu
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Abstract

We construct one-dimensional foliations which are subfoliations of two-dimensional foliations in $3$ -manifolds. The subfoliation is by quasigeodesics in each two-dimensional leaf, but it is not funnel: not all quasigeodesics share a common ideal point in most leaves.

Keywords

quasigeodesicssubfoliationsAnosov flows

MSC classification

Primary: 37C10: Vector fields, flows, ordinary differential equations 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 57R30: Foliations; geometric theory 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 37D45: Strange attractors, chaotic dynamics 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification 37D10: Invariant manifold theory
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 8 , August 2023 , pp. 2624 - 2650
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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