Deterministic quantum noise and Kolmogorov systems

Two irreversible quantum evolutions with zero dynamical entropy, when dilated to reversible automorphisms, provide quantum Kolmogorov systems of both the algebraic and entropic type with infinite-dynamical entropy.     

Chaos and irreversibility in simple model systems

The multifractal link between chaotic time-reversible mechanics and thermodynamic irreversibility is illustrated for three simple chaotic model systems: the Baker Map, the Galton Board, and many-body color conductivity. By scaling time, or the momenta, or the driving forces, it can be shown that the dissipative nature of the three thermostated model systems has analogs in conservative Hamiltonian and Lagrangian mechanics. Links between the microscopic nonequilibrium Lyapunov spectra and macroscopic thermodynamic dissipation are also pointed out. (c) 1998 American Institute of Physics.     

Resynchronizing dynamical systems

Resynchronizing dynamical systems are important for certain chaotic signal masking methods. We demonstrate the dependence of the resynchronizing property of linear dynamical systems on choices of coordinate systems. Using these insights, we demonstrate how a nonlinear system not previously known to be synchronizable can be used for chaotic signal masking.     

Non-Hamiltonian dynamical systems

The class of dynamical systems is considered, which are described by several mutually noncommuting Hamiltonian currents, in particular, relativistic bi-Hamiltonian systems, the evolution of which is described by a pair of 4-momenta p and p The examination is conducted in classical and quantum realizations. The evolution equations are derived of relativistic bi-Hamiltonian systems in the Heisenberg and Schrödinger pictures. It is shown that the quantum theory of relativistic bi-Hamiltonian systems is not compatible with the unitary condition and is nonunitary. A physical interpretation is given of nonunitary quantum theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 5–12, October, 1990.     

General kinetic equation and irreversibility in statistical systems

General kinetic equation for statistical systems is presented. A kinetic equation with source that is fluctuation of physical values was obtained. A new statistical criterion of systems evolution was determined. Nonequilibrium statistical and variational derivations of general kinetic equations are considered. Evolution of nonequilibrium Boltzmann-Gibbs-Shannon entropy, Hamilton function and Hamilton function production are examined.     

Remarks on entropy and irreversibility in non-hamiltonian systems

Entropy and irreversibility in non-hamiltonian systems are discussed from a fully covariant point of view. The discussion is based on the generalized Liouville equation, the definition of a volume element dV in state space, and a generalized hypothesis of equal a priori probabilities. Systems may be classified as reversible or irreversible according to whether it is or is not possible to define dV so that the flow is globally volume-preserving in state space.     

Iterated function systems and dynamical systems

We study the relationship between measures invariant for a piecewise expanding transformation tau of a compact metric space endowed with a underlying measure and measures invariant for an iterated function system T(tau), generated by inverse branches of tau. The main result says that the tau-invariant absolutely continuous measure &mgr; is also T(tau) invariant if and only if tau is absolutely continuously conjugated with a piecewise linear transformation. Measures of maximal entropy and general equilibrium states are also discussed. (c) 1995 American Institute of Physics.     

New solvable dynamical systems

New solvable dynamical systems are identified and the properties of their solutions are tersely discussed.     

Topology in dynamical systems

Previously the torsion number and the relative torsion number have been introduced to describe the topological character of periodic solutions of a three-dimensional ordinary differential equation. In this letter, considering the rewinding mechanism of tangent vectors, we investigate the change of the torsion numbers and the relative torsion numbers as period-doubling bifurcation cascades.     

Punctures and dynamical systems

Letters in Mathematical Physics - With the aim of better understanding the class of 4D theories generated by compactifications of 6D superconformal field theories (SCFTs), we study the structure of...     

Measure of irreversibility and entropy production in open quantum systems

A new concept of a measure of irreversibility for quantum dynamics in open systems is introduced as a suitably regularized substitute for the common notion of entropy production, which, unfortunately, yields infinite values for so many irreversible processes of physical relevance.     

Analytic structure of dynamical systems

The study of the analytic structure of nonlinear ordinary and partial differential equations is shown to provide a unified approach to determining their properties and finding their solutions. A course of lectures delivered at the School on Chaos and Nonlinear Dynamics held at the Indian Institute of Science, Bangalore, India (June 24th–July 18th 1987)     

Synchronization of reconstructed dynamical systems

The problem of constructing synchronizing systems to observed signals is approached from a data driven perspective, in which it is assumed that neither the drive nor the response systems are known explicitly but have to be derived from the observations. The response systems are modeled by utilizing standard methods of nonlinear time series analysis applied to sections of the driving signals. As a result, synchronization is more robust than what might be expected, given that the reconstructed systems are only approximations of the unknown true systems. Successful synchronization also may be accomplished in cases where the driving signals result from nonlinearly transformed chaotic states. The method is readily extended and applied to limited real-time predictions of chaotic signals.     

On the dynamics of a class of rational Kolmogorov systems

In this paper we are intersted in studying the existence of a First integral and the non-existence of limit cycles of rational Kolmogorov systems of the form where P (x, y) , Q (x, y) , R (x, y) , S (x, y) are homogeneous polynomials of degree n, n, m, a respectively.