Subexponential instability implies infinite invariant measure

Abstract

We study subexponential instability to characterize a dynamical instability of weak chaos. We show that a dynamical system with subexponential instability has an infinite invariant measure, and then we present the generalized Lyapunov exponent to characterize subexponential instability.

7 pages, 5 figures

References in corpus (4)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Pesin-Type Identity for Weak Chaos
• Exact analytic solution for the generalized Lyapunov exponent of the 2-dimensional Anderson localization
• On the definition of equilibrium and non-equilibrium states in dynamical systems

Cited by in corpus (16)

• Distributional Response to Biases in Deterministic Superdiffusion
• Aging generates regular motions in weakly chaotic systems
• Phase Diagram in Stored-Energy-Driven Lévy Flight
• Infinite Invariant Density Determines Statistics of Time Averages for Weak Chaos
• Infinite invariant density in a semi-Markov process with continuous state variables
• Distributional behavior of time averages of non-$L^1$ observables in one-dimensional intermittent maps with infinite invariant measures
• Exact Lyapunov exponents of the generalized Boole transformations
• Pesin-type relation for subexponential instability
• Aging arcsine law in Brownian motion and its generalization
• Generalized Lyapunov exponent as a unified characterization of dynamical instabilities
• Lyapunov statistics and mixing rates for intermittent systems
• Numerical estimate of infinite invariant densities: application to Pesin-type identity
• Infinite Ergodicity that Preserves the Lebesgue Measure
• Dynamical Instability and Transport Coefficient in Deterministic Diffusion
• Quantitative universality for a class of weakly chaotic systems
• Does an intermittent dynamical system remain (weakly) chaotic after drilling in a hole?