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The orbit of a Hölder continuous path under a hyperbolic toral automorphism

Published online by Cambridge University Press:  19 September 2008

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

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Let f:T3→T3 be a hyperbolic toral automorphism lifting to a linear automorphism with real eigenvalues. We prove that there is a Hölder continuous path in T3 whose orbit-closure is 1-dimensional. This strengthens results of Hancock and Przytycki concerning continuous paths, and contrasts with results of Franks and Mañé concerning rectifiable paths.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 3 , September 1983, pp. 345 - 349
Copyright
Copyright © Cambridge University Press 1983

References

REFERENCES

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