Bounds on Lyapunov Exponents via Entropy Accumulation

Entropy potential and Lyapunov exponents.

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function, the entropy potential. The validity and the consequences of this hypothesis are explored in detail. The numerical investigation of a continuous-time model provides a further confirmation to the existence of the entropy potential. Furthe...

Lyapunov Exponents, Entropy Production, and Decoherence

We establish that the entropy production rate of a classically chaotic Hamiltonian system coupled to the environment settles, after a transient, to a metastable value given by the sum of positive generalized Lyapunov exponents. A metastable steady state is generated in this process. This behavior also occurs in quantum systems close to the classical limit, where it leads to the restoration of q...

On Entropy and Lyapunov Exponents for Finite-State Channels

The Finite-State Markov Channel (FSMC) is a time-varying channel having states that are characterized by a finite-state Markov chain. These channels have infinite memory, which complicates their capacity analysis. We develop a new method to characterize the capacity of these channels based on Lyapunov exponents. Specifically, we show that the input, output, and conditional entropies for this ch...

Lectures on Lyapunov exponents

Nonhyperbolic Step Skew-products: Entropy Spectrum of Lyapunov Exponents

We study the fiber Lyapunov exponents of step skew-product maps over a complete shift of N , N ≥ 2, symbols and with C1 diffeomorphisms of the circle as fiber maps. The systems we study are transitive and genuinely nonhyperbolic, exhibiting simultaneously ergodic measures with positive, negative, and zero exponents. We derive a multifractal analysis for the topological entropy of the level sets...