Singularities in Rényi information as phase transitions in chaotic states
- 1 May 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 39 (9) , 4767-4777
- https://doi.org/10.1103/physreva.39.4767
Abstract
Chaotic dynamical systems are investigated, with the help of the Rényi information concept, both in their phase space and in their history space. Several phases are distinguished and their characteristics are discussed. Emphasis is put on two particular situations representing borderline cases of chaos: when an unstable periodic orbit exists in the system with a zero or an infinite Lyapunov exponent.Keywords
This publication has 22 references indexed in Scilit:
- Anomalous scaling laws in multifractal objectsPhysics Reports, 1987
- Phase transitions associated with dynamical properties of chaotic systemsPhysical Review A, 1987
- Phase transitions in the thermodynamic formalism of multifractalsPhysical Review Letters, 1987
- Information and information gain close to nonequilibrium phase transitions. Numerical resultsZeitschrift für Physik B Condensed Matter, 1986
- Fractal measures and their singularities: The characterization of strange setsPhysical Review A, 1986
- Information, information gain, and efficiency of self-organizing systems close to instability pointsZeitschrift für Physik B Condensed Matter, 1985
- Is the dimension of chaotic attractors invariant under coordinate changes?Journal of Statistical Physics, 1984
- Information Dimension and the Probabilistic Structure of ChaosZeitschrift für Naturforschung A, 1982
- A Mathematical Theory of CommunicationBell System Technical Journal, 1948
- A Mathematical Theory of CommunicationBell System Technical Journal, 1948