MARK POLLICOTT and HOWARD WEISS
Multifractal analysis for the continued fraction and 
Manneville-Pomeau transformations and applications to 
Diophantine Approximation
(732K, Postscript)

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.