- 98-688 MARK POLLICOTT and HOWARD WEISS
- Multifractal analysis for the continued fraction and
Manneville-Pomeau transformations and applications to
Oct 29, 98
(auto. generated ps),
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.