A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions
Journal Article
·
· Journal of Statistical Physics
- 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, Vol. 86, Issue 1-2; Other Information: PBD: Jan 1997
- Country of Publication:
- United States
- Language:
- English
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