Dynamical spectrum and thermodynamic functions of strange sets from an eigenvalue problem

Publisher Website
Google Scholar
Abstract
The dynamical multifractal spectrum of hyperbolic systems is found to be the fundamental equation in a kind of statistical-mechanics formalism for both permanent and transient chaos. It is shown that the free energy may appear in an eigenvalue problem, the solution to which provides a new method for calculating dynamical spectra. Explicit examples are given and the possibility of extending the method for higher-dimensional systems is discussed.