in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schrödinger equation. This nonintegrable model, ubiquitous in several fields physics, describes behavior an array coupled complex oscillators with local potential. explore Lyapunov spectrum for different values energy density, finding that maximal value Kolmogorov-Sinai entropy is attained at infinite temperatures. Moreover...

Replication and differentiation of spots in a class of reaction–diffusion equations are studied by extending the Gray–Scott model with self-replicating spots so that it includes many chemical species. By examining many possible reaction networks, the behavior of this model is categorized into three types: replication of homogeneous fixed spots, replication of oscillatory spots, and differentiat...

This paper is dedicated to the statistical analysis of the chaos, generated by Rössler attractor, based on the socalled “Degenerated Cumulant Equations” method. The approach is illustrated by the calculus of the first cumulants, which are necessary to create an approximation of the Probability Density Function (PDF), applying the Gramm-Charlier series, the model distribution method, etc. An app...

We introduce a deterministic chaotic system-the Szilard map-that encapsulates the measurement, control, and erasure protocol by which Maxwellian demons extract work from a heat reservoir. Implementing the demon's control function in a dynamical embodiment, our construction symmetrizes the demon and the thermodynamic system, allowing one to explore their functionality and recover the fundamental...

Let a countable amenable group G acts freely and ergodically on a Lebesgue space (X;), preserving the measure. If T 2 Aut (X;) is an automorphism of the equivalence relation deened by G then T can be extended to an automorphism T of the II 1-factor M = L 1 (X;)oG. We prove that if T commutes with the action of G then H(T) = h(T), where H(T) is the Connes-Sttrmer entropy of T , and h(T) is the K...

We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e., the disordered Lorentz gas, in a generic nonequilibrium situation. In a large system which is finite in at least some directions, and with absorbing boundary conditions, the moving particle escapes the system with probability one. However, there is a ...

In this paper, we discuss the properties of making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy, high dimensionality of the parent dynamical system, and very large period of the generated sequence. We propose the chaotic coupled map lattices as a pseudo random number generator. We show what chaotic features of the cou...

Let a countable amenable group G acts freely and ergodically on a Lebesgue space (X;), preserving the measure. If T 2 Aut (X;) is an automorphism of the equivalence relation deened by G then T can be extended to an automorphism T of the II 1-factor M = L 1 (X;)oG. We prove that if T commutes with the action of G then H(T) = h(T), where H(T) is the Connes-Sttrmer entropy of T , and h(T) is the K...

A coupled map model for cloud dynamics is proposed, which consists of the successive operations of the physical processes; buoyancy, diusion, viscosity, adi-abatic expansion, fall of a droplet by gravity, descent ow dragged by the falling droplet, and advection. Through extensive simulations, the phases corresponding to stratus, cumulus, stratocumulus and cumulonimbus are found, with the change...