Chaotic family with smooth Lyapunov dependence
- 1 June 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 55 (6) , 7763-7766
- https://doi.org/10.1103/physreve.55.7763
Abstract
A smooth dependence of the Lyapunov exponent is proved for a nontrivial family of chaotic maps. The approach that is taken demonstrates the importance of Markov partitions in connection with the thermodynamic analysis for dynamical systems.Keywords
This publication has 15 references indexed in Scilit:
- Superpositions of multifractals: Generators of phase transitions in the generalized thermodynamic formalismJournal of Statistical Physics, 1996
- Simple Maps with Fractal Diffusion CoefficientsPhysical Review Letters, 1995
- Using small perturbations to control chaosNature, 1993
- Synchronization of chaotic trajectories using controlPhysical Review E, 1993
- Statistical properties of chaos demonstrated in a class of one-dimensional mapsChaos: An Interdisciplinary Journal of Nonlinear Science, 1993
- Phase-transition-like phenomenon in a piecewise linear mapPhysica A: Statistical Mechanics and its Applications, 1990
- Controlling chaosPhysical Review Letters, 1990
- Evaluation of Lyapunov exponents and scaling functions from time seriesJournal of the Optical Society of America B, 1988
- The transition to aperiodic behavior in turbulent systemsCommunications in Mathematical Physics, 1980
- The universal metric properties of nonlinear transformationsJournal of Statistical Physics, 1979