Rare Events for Cantor Target Sets

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Ana Cristina Moreira Freitas (Author) FEP; Jorge Milhazes Freitas (Author) FCUP; Rodrigues, FB (Author) Other; Soares, JV (Author) Other

Journal

Title: Communications in Mathematical Physics

Vol. 378 No. 1

Pages: 75-115

ISSN: 0010-3616

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 6 Citations

Other information

Authenticus ID: P-00S-DHR

DOI: 10.1007/s00220-020-03794-1

Abstract (EN): We study the existence of limiting laws of rare events corresponding to the entrance of the orbits on certain target sets in the phase space. The limiting laws are obtained when the target sets shrink to a Cantor set of zero Lebesgue measure. We consider both the presence and absence of clustering, which is detected by the Extremal Index, which turns out to be very useful to identify the compatibility between the dynamics and the fractal structure of the limiting Cantor set. The computation of the Extremal Index is connected to the box dimension of the intersection between the Cantor set and its iterates.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 41