Looking at the equilibrium measures in dynamical systems

Publisher Website
Google Scholar
Abstract
The authors discuss how finite-time fluctuations of the chaoticity degree permit one to observe a family of equilibrium measures defined in the thermodynamical formalism for expanding one-dimensional maps and for axion A systems. By means of generalised Lyapunov exponents one can thus calculate the Kolmogorov entropies, the Lyapunov exponents and the Hausdorff dimensions for this set of measures. They perform such a calculation for the Lozi map, an almost everywhere hyperbolic diffeomorphism of the plane. They stress the heuristic power of their approach, which can be extended to more generic non-hyperbolic systems. In this case they suggest that phase transition phenomena might appear as a consequence of the existence of 'laminar-like' regular periods during chaotic evolutions.

This publication has 20 references indexed in Scilit: