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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
Abstract
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.
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- Copyright © Cambridge University Press 1983
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