Dimension Spectra of Hyperbolic Flows

Autor:	Luis Barreira, Paulo Doutor
Rok vydání:	2009
Předmět:	Pure mathematics Mathematics::Dynamical Systems Markov chain Mathematical analysis Statistical and Nonlinear Physics Multifractal system Fractal Discrete time and continuous time Variational principle Iterated function Hyperbolic set Countable set Mathematical Physics Mathematics
Zdroj:	Journal of Statistical Physics. 136:505-525
ISSN:	1572-9613 0022-4715
DOI:	10.1007/s10955-009-9790-5
Popis:	For flows with a conformal hyperbolic set, we establish a conditional variational principle for the dimension spectra of Holder continuous functions. We consider simultaneously Birkhoff averages into the future and into the past. We emphasize that the description of the spectra is not a consequence of the existing results for Birkhoff averages into the future (or into the past). The main difficulty is that even though the local product structure is bi-Lipschitz, the level sets of the Birkhoff averages are never compact. Our proof is based on the use of Markov systems and is inspired in earlier arguments in the case of discrete time.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4e7b1669f3463e533602ca5c6cee1439 https://doi.org/10.1007/s10955-009-9790-5 Zobrazit plný text záznamu Plný text ve formátu PDF