On large deviations for some dynamical systems and for Gibbs states at zero temperature

MESON, ALEJANDRO M.; VERICAT, FERNANDO

JOURNAL OF DYNAMICAL SYSTEMS AND GEOMETRIC THEORIES

Taru Publications

Lugar: New Dehli; Año: 2011 vol. 9 p. 151 - 164

1726-037X

In this article we analyze two issues related with large deviations in dynamical systems:1.We show that the level-2 large deviation principle established by Comman and Rivera-Letelier is satisfied by maps with a specification property and, with some additional condition, by those with the almost property product, which is weaker than specification. The earlier mentioned  authors proved that their principle, which is a generalization of previous results by Kifer, is verified by a class of hyperbolic rational maps.2. In a previous article we have considered a family of Gibbs states which had a zero temperature accumulation point. We proved that this accumulation point is a maximizing measure for more general systems than symbolics. In a recent article by Lopes and Mengue were considered similar families of states and proved, for symbolic dynamics, that an accumulation point of the family was maximizing. Also they established a large deviation principle. In this note we show how to use the results of our previous work to describe a large deviation process in a more general context than that of Lopes and Mengue.