Multifractal analysis of the Lyapunov exponent for the backward continued fraction map

DOI10.1017/S0143385708001090zbMath1184.37038arXiv0812.1745MaRDI QIDQ5188014

Godofredo Iommi

Publication date: 10 March 2010

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.1745

zbMATH Keywords

interval mapLyapunov exponentMarkov shift

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems involving maps of the interval (37E05)

Related Items (12)

The Lyapunov spectrum is not always concave ⋮ The thermodynamic approach to multifractal analysis ⋮ Dimension estimates for arbitrary subsets of limit sets of a Markov construction and related multifractal analysis ⋮ Slow continued fractions, transducers, and the Serret theorem ⋮ Level-2 large deviation principle for countable Markov shifts without Gibbs states ⋮ The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps ⋮ Dimension theory for multimodal maps ⋮ Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches ⋮ How many inflections are there in the Lyapunov spectrum? ⋮ Frequency of digits in the Lüroth expansion ⋮ Large deviation principle for the backward continued fraction expansion ⋮ Counting the Lyapunov inflections in piecewise linear systems*

Cites Work

• Unnamed Item
• More on inhomogeneous Diophantine approximation
• A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates
• Invariant measures for general(ized) induced transformations
• Thermodynamic Formalism
• Backward continued fractions, Hecke groups and invariant measures for transformations of the interval
• Multifractal analysis for countable Markov shifts
• Ergodic optimization for countable alphabet subshifts of finite type

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