Hausdorff dimension of a Cantor set on \(\mathbb{R}^1\)

DOI10.3836/TJM/1244208596zbMath1035.37018OpenAlexW1977710032MaRDI QIDQ1429088

Makoto Mori, Mariko Ohno, Yuko Ichikawa

Publication date: 30 March 2004

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1244208596

zbMATH Keywords

Cantor setHausdorff dimensionMarkov chainMarkov transformationspiecewise linear transformations

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Fractals (28A80) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Dimension theory of smooth dynamical systems (37C45)

Cites Work

• Unnamed Item
• Unnamed Item
• Fredholm determinant for piecewise linear transformations
• Dynamical system on Cantor set
• Fredholm determinant for piecewise linear transformations on a plane
• Fredholm determinant for piecewise monotonic transformations
• Computing the dimension of dynamically defined sets: E_2 and bounded continued fractions
• Zeta-functions and transfer-operators for piecewise linear transformations.
• On the Existence of Invariant Measures for Piecewise Monotonic Transformations
• Dynamical systems on fractals in a plane

This page was built for publication: Hausdorff dimension of a Cantor set on \(\mathbb{R}^1\)