Statistical-thermodynamic approach to a chaotic dynamical system: exactly solvable examples.

DOI10.1007/BF01015570zbMath1083.37513MaRDI QIDQ1963693

H. Shigematsu

Publication date: 2 February 2000

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

chaosphase transitionthermodynamic approachscaling lawlocal Lyapunov exponentsymbol sequencegeneralized entropynatural measureone-dimensional lattice systemgeneralized dimensionnonhyperbolic attractorscaling index

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Statistical thermodynamics (82B30) Dynamical aspects of statistical mechanics (37A60)

Related Items (1)

Phase transitions in thermodynamics of a local Lyapunov exponent for fully-developed chaotic systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Scaling spectra and return times of dynamical systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Is the dimension of chaotic attractors invariant under coordinate changes?
• Phase transitions in thermodynamics of a local Lyapunov exponent for fully-developed chaotic systems
• Generalized dimensions, entropies, and Lyapunov exponents from the pressure function for strange sets.
• Scaling laws for invariant measures on hyperbolic and nonhyperbolic attractors.
• Statistical Dynamics Generated by Fluctuations of Local Lyapunov Exponents
• Towards the Statistical Mechanics of Chaos
• Fractal measures and their singularities: The characterization of strange sets
• Scaling structure and thermodynamics of strange sets
• Ergodic theory of chaos and strange attractors

This page was built for publication: Statistical-thermodynamic approach to a chaotic dynamical system: exactly solvable examples.