Geodesic flow, connecting orbits and almost full foliation
type: Item
instance of: scholarly article
title: Geodesic flow, connecting orbits and almost full foliation
zbMATH Open document ID: 1116.53060
author: Jian Cheng
author: Long Meng
published in: Science in China. Series A
publication date: 2007-03-14T00:00:00Z
review text: Considering the geodesic flow of the torus \(\mathbb{T}^2\), endowed with a metric which is a certain local deformation of the flat one, the authors exhibit an example for which the following special complicated dynamical behaviour holds: \(\bullet\) the set of minimal geodesics having a given average slope can have Hausdorff dimension 2 (in the unit tangent bundle); \(\bullet\) any two minimal sets with different rational slopes can be connected by some orbit.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 37C27
Mathematics Subject Classification ID: 37C55
Mathematics Subject Classification ID: 37C45
zbMATH DE Number: 5133946
zbMATH Keywords: geodesic flows
zbMATH Keywords: rotation numbers
zbMATH Keywords: minimal configurations
zbMATH Keywords: connecting orbits
MaRDI profile type: Publication
full work available at URL: s11425-006-1831-9
OpenAlex ID: W1571936154
cites work: Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
cites work: Variational Construction of Orbits of Twist Diffeomorphisms
cites work: Variational approach to homoclinic orbits in twist maps and an application to billiard systems
cites work: Q3814339
cites work: Curvature Bounds for the Entropy of the Geodesic Flow on a Surface
cites work: Q3952851
DOI: 10.1007/S11425-006-1831-9
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description: scientific article; zbMATH DE number 5133946