A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions

Journal Article · Tue Dec 31 23:00:00 EST 1996 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02180206· OSTI ID:468669

Pesin, Y; Weiss, H ^[1]

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1. Pennsylvania State Univ., University Park, PA (United States)

In this paper we establish the complete multifractal formalism for equilibrium measures for Holder continuous conformal expanding maps and expanding Markov Moran-like geometric constructions. Examples include Markov maps of an interval, beta transformations of an interval, rational maps with hyperbolic Julia sets, and conformal total endomorphisms. We also construct a Holder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex, and hence the multifractal formalism fails.

• Sponsoring Organization: USDOE
• OSTI ID: 468669
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1-2 Vol. 86; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
ATTRACTORS
CONFORMAL MAPPING
ENTROPY
FRACTALS
MARKOV PROCESS