Ergodic transport theory and piecewise analytic subactions for analytic dynamics

Autor(es)

Lopes, A. O. ^[1] ; Oliveira, E. R. ^[1] ; Smania, D. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Rio Grande do Sul, Inst Matemat, BR-91509900 Porto Alegre, RS - Brazil

^[2] ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 43, n. 3, p. 467-512, SEP 2012.
• Citações Web of Science: 3

Resumo

We consider a piecewise analytic real expanding map f: {[}0, 1] -> {[}0, 1] of degree d which preserves orientation, and a real analytic positive potential g: {[}0, 1] -> a{''}e. We assume the map and the potential have a complex analytic extension to a neighborhood of the interval in the complex plane. We also assume log g is well defined for this extension. It is known in Complex Dynamics that under the above hypothesis, for the given potential beta log g, where beta is a real constant, there exists a real analytic eigenfunction I center dot (beta) defined on {[}0, 1] (with a complex analytic extension) for the Ruelle operator of beta log g. Under some assumptions we show that converges and is a piecewise analytic calibrated subaction. Our theory can be applied when log g(x) = -log f'(x). In that case we relate the involution kernel to the so called scaling function. (AU)

• Processo FAPESP: 08/02841-4 - Teoria topológica, geométrica e ergódica dos sistemas dinâmicos
• Beneficiário: Jorge Manuel Sotomayor Tello
• Modalidade de apoio: Auxílio à Pesquisa - Temático