We investigate the relations holding among generalized dimensions of invariant measures in dynamical systems and similar quantities defined by the scaling of global averages of powers of return times. Because of a heuristic use of Kac theorem, these latter have been used in place of the former in numerical and experimental investigations; to mark this distinction, we call them return time dimensions. We derive a full set of inequalities linking measure and return time dimensions and we comment on their optimality with the aid of two maps due to von Neumann -- Kakutani and to Gaspard -- Wang. We conjecture the behavior of return time dimensions in a typical system. We only assume ergodicity of the dynamical system under investigation.
|Data di pubblicazione:||2010|
|Titolo:||The global statistics of return times: return time dimensions versus generalized measure dimensions|
|Rivista:||JOURNAL OF STATISTICAL PHYSICS|
|Codice identificativo ISI:||WOS:000274949900008|
|Codice identificativo Scopus:||2-s2.0-77249101484|
|Parole Chiave:||Renyi spectrum; Hentschel-Procaccia dimensions; Return times; Return times dimensions|
|Appare nelle tipologie:||Articolo su Rivista|