Lyapunov spectrum for geodesic flows of rank 1 surfaces

Keith Burns; Katrin Gelfert

doi:10.3934/dcds.2014.34.1841

Lyapunov spectrum for geodesic flows of rank 1 surfaces

Keith Burns, Katrin Gelfert

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We give estimates on the Hausdoff dimension of the levels sets of the Lyapunov exponent for the geodesic flow of a compact rank 1 surface. We show that the level sets of points with small (but non-zero) exponents has full Hausdorff dimension, but carries small topological entropy.

Original language	English (US)
Pages (from-to)	1841-1872
Number of pages	32
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	34
Issue number	5
DOIs	https://doi.org/10.3934/dcds.2014.34.1841
State	Published - May 2014

Keywords

Entropy
Geodesic flow
Hausdorff dimension
Lyapunov exponents
Multifractal formalism
Pressure
Rank 1 surfaces
Shadowing

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2014.34.1841

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title = "Lyapunov spectrum for geodesic flows of rank 1 surfaces",

abstract = "We give estimates on the Hausdoff dimension of the levels sets of the Lyapunov exponent for the geodesic flow of a compact rank 1 surface. We show that the level sets of points with small (but non-zero) exponents has full Hausdorff dimension, but carries small topological entropy.",

keywords = "Entropy, Geodesic flow, Hausdorff dimension, Lyapunov exponents, Multifractal formalism, Pressure, Rank 1 surfaces, Shadowing",

author = "Keith Burns and Katrin Gelfert",

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KW - Entropy

KW - Geodesic flow

KW - Hausdorff dimension

KW - Lyapunov exponents

KW - Multifractal formalism

KW - Pressure

KW - Rank 1 surfaces

KW - Shadowing

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Lyapunov spectrum for geodesic flows of rank 1 surfaces

Abstract

Keywords

ASJC Scopus subject areas

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