TITLE:
Multifractal Analysis of the Asympyotically Additive Potentials
AUTHORS:
Lan Xu, Long Yang
KEYWORDS:
Multifractal Analysis, u-Dimension Spectra, Asymptotically Additive
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.13,
December
22,
2014
ABSTRACT: Multifractal analysis studies level sets of asymptotically defined
quantities in dynamical systems. In this paper, we consider the u-dimension spectra on such level
sets and establish a conditional variational principle for general
asymptotically additive potentials by requiring only existence and uniqueness
of equilibrium states for a dense subspace of potential functions.