Lyapunov Spectrum of Asymptotically Sub-additive Potentials
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AbstractFor general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measure-theoretic entropies and topological pressures in this general situation. Most of our results are obtained without the assumption of the existence of unique equilibrium measures or the differentiability of pressure functions. Some examples are constructed to illustrate the irregularity and the complexity of multifractal behaviors in the sub-additive case and in the case that the entropy map is not upper-semi continuous.
All Author(s) ListFeng DJ, Huang W
Journal nameCommunications in Mathematical Physics
Volume Number297
Issue Number1
PublisherSpringer Verlag (Germany)
Pages1 - 43
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesPhysics; Physics, Mathematical; PHYSICS, MATHEMATICAL

Last updated on 2020-24-10 at 00:33