IFLYSIB   05383
INSTITUTO DE FISICA DE LIQUIDOS Y SISTEMAS BIOLOGICOS
Unidad Ejecutora - UE
artículos
Título:
On the irregular part of V-statistics multifractal spectra for systems with non-uniform specification
Autor/es:
MESON, ALEJANDRO M.; VERICAT, FERNANDO
Revista:
JOURNAL OF DYNAMICAL SYSTEMS AND GEOMETRIC THEORIES
Editorial:
Taylor & Francis
Referencias:
Lugar: New Dehli; Año: 2015 vol. 13 p. 1 - 26
ISSN:
1726-037X
Resumen:
Let (X,f) be a dynamical system with X a compact metric space. Let X^{r} be the product of r-copies of X, r≥1, and Φ:X^{r} →R. The multifractal decomposition for V-statistics for Φ,f is defined as E_{Φ,f}(α)={x:lim_{n→∞}(1/(n^{r}))∑_{0≤i₁,...,i_{r}≤n-1}Φ(f^{i₁}(x),...,f^{i_{r(x))=α}. The set of points x∈X, for which the limit does not exist is called the irregular part, or historic set, of the spectrum. In this article we analyze the irregular part of the V-statistics for systems satisfying a weak form of the known Bowen specification property, called the non-uniform specification property. This concept was introduced by P. Varandas and allows to work in a nonuniformly hyperbolic context.