Extreme values for Benedicks-Carleson quadratic maps

• Tipo: Artigo em Revista Científica Internacional
• Data: 2008

Autores

Ana Cristina M Moreira Freitas (Autor) FEP; Jorge Milhazes Freitas (Autor) FCUP

Revista

Título: Ergodic Theory and Dynamical Systems

Vol. 28 Nº 4

Páginas: 1117-1133

ISSN: 0143-3857

Editora: Cambridge University Press

Indexação

ISI Web of Knowledge - 23 Citações

ISI Web of Science

Scopus - 24 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

CORDIS: Ciências Físicas > Matemática > Teoria do caos

Outras Informações

ID Authenticus: P-003-X76

DOI: 10.1017/s0143385707000624

Abstract (EN): We consider the quadratic family of maps given by f(a)(x) = 1 - ax(2) with x epsilon [- 1, 1], where a is a Benedicks-Carleson parameter. For each of these chaotic dynamical systems we study the extreme value distribution of the stationary stochastic processes X(0), X(1), ..., given by X(n) = f(a)(n), for every integer n >= 0, where each random variable Xn is distributed according to the unique absolutely continuous, invariant probability of f(a). Using techniques developed by Benedicks and Carleson, we show that the limiting distribution of M(n) = max {X(0), ..., X(n) - 1} is the same as that which would apply if the sequence X(0), X(1), ... was independent and identically distributed. This result allows us to conclude that the asymptotic distribution of M(n) is of type III (Weibull).

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 17