98-688 MARK POLLICOTT and HOWARD WEISS

Multifractal analysis for the continued fraction and Manneville-Pomeau transformations and applications to Diophantine Approximation (732K, Postscript) Oct 29, 98

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. In this note 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 apply the multifractal analysis to prove some new results on the precise exponential speed of convergence of the continued fraction algorithm. This gives new quantitative information on geodesic excursions up cusps on the modular surface.

Files: 98-688.src( 98-688.keywords , multi.ps )