Entropy computing via integration over fractal measures

Abstract

We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with certain dynamical systems one can associate the corresponding IFSs in such a way that their generalized entropies are equal. This provides a new method of computing entropy for some classical and quantum dynamical systems. Numerical techniques are based on integration over the fractal measures.

14 pages in Latex, Revtex + 4 figures in .ps attached (revised version, new title, several changes, to appear in CHAOS)

References in corpus (2)

• Mean dynamical entropy of quantum system tends to infinity in the semiclassical limit
• Dynamical entropy for systems with stochastic perturbation

Cited by in corpus (8)

• Quantum Iterated Function Systems
• Shannon Entropy Rate of Hidden Markov Processes
• Dynamical entropy for systems with stochastic perturbation
• Divergent Predictive States: The Statistical Complexity Dimension of Stationary, Ergodic Hidden Markov Processes
• Follow-the-Regularized-Leader Routes to Chaos in Routing Games
• Notes on use of generalized entropies in counting
• Parry measure and the topological entropy of chaotic repellers embedded within chaotic attractors
• Informational and entropic criteria of self-organization