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Hölder continuous paths and hyperbolic toral automorphisms

Published online by Cambridge University Press:  19 September 2008

M. C. Irwin
M. C. Irwin
Affiliation:
Department of Pure Mathematics, Liverpool University, Liverpool, L69 3BX, England
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Abstract

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Let f:Tn→Tn (n ≥ 3) be a hyperbolic toral automorphism. Let A be the set of α > 0 such that there is a Hölder continuous path of index α in Tn with 1-dimensional orbit-closure under f We prove that α0 = sup A can be expressed in terms of the eigenvalues of f and that α0 ∈ A if and only if α0 < 1.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 2 , June 1986 , pp. 241 - 257
Copyright
Copyright © Cambridge University Press 1986

References

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