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Piecewise contracting maps on the interval: Hausdorff dimension, entropy, and attractors
Published online by Cambridge University Press: 21 September 2023
Abstract
We consider the attractor $\Lambda $ of a piecewise contracting map f defined on a compact interval. If f is injective, we show that it is possible to estimate the topological entropy of f (according to Bowen’s formula) and the Hausdorff dimension of $\Lambda $ via the complexity associated with the orbits of the system. Specifically, we prove that both numbers are zero.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society
Footnotes
A.E.C. was supported by ANID Fondecyt Iniciación N°11230064, ANID Fondecyt Regular N°1230569, MathAmsud Project VOS 22-MATH-08, and MathAmsud Project TOMCAT 22-MATH-10. E.V-S. was supported by Ph.D. funding from ANID, Beca Chile Doctorado en el Extranjero (Grant No. 72210071).