Multifractal analysis of lyapunov exponent for continued fraction and Manneville-Pomeau transformations and applications to diophantine approximation

Mark Pollicott, Howard Weiss

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Abstract

We extend some of the theory of multifractal analysis for conformal expanding systems to two new cases: The non-uniformly hyperbolic example of the Manneville-Pomeau equation and the continued fraction transformation. A common point in the analysis is the use of thermodynamic formalism for transformations with infinitely many branches. We effect a complete multifractal analysis of the Lyapunov exponent for the continued fraction transformation and as a consequence obtain some new results on the precise exponential speed of convergence of the continued fraction algorithm. This analysis also provides new quantitative information about cuspital excursions on the modular surface.

Original languageEnglish (US)
Pages (from-to)145-171
Number of pages27
JournalCommunications In Mathematical Physics
Volume207
Issue number1
DOIs
Publication statusPublished - Jan 1 1999

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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