Extreme Value Laws in Dynamical Systems for Non-smooth Observations

• Type: Article in International Scientific Journal
• Date: 2011

Authors

Ana Cristina M Moreira Freitas (Author) FEP; Jorge Milhazes Freitas (Author) FCUP; Mike Todd (Author) Other

Journal

Title: Journal of Statistical Physics

Vol. 142

Pages: 108-126

ISSN: 0022-4715

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 56 Citations

ISI Web of Science

Scopus - 59 Citations

Scientific classification

FOS: Natural sciences > Physical sciences

Other information

Authenticus ID: P-002-XVC

DOI: 10.1007/s10955-010-0096-4

Abstract (EN): We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue. This is a counterpart to the result of the authors in the absolutely continuous case. Moreover, we prove an equivalent result for returns to dynamically defined cylinders. This allows us to show that we have Extreme Value Laws for various dynamical systems with equilibrium states with good mixing properties. In order to achieve these goals we tailor our observables to the form of the measure at hand.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19