Results 1 - 10 of 526
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[en] First we try to generalize the notion of a topological transitive or a topologically mixing system for quantum mechanical systems in a consistent way. Furthermore we compare these ergodic properties with the classical results. Finaly we deal with some aspects of nearly abelian systems and investigate some relations between these notions. 11 refs. (Author)
[en] The aim of this paper is to relate the almost average shadowing property (ALASP) with various variants of ergodicity and with some other dynamical properties. We also study the relation of the ALASP with proximality.
[en] The problem of transforming autonomous systems into Birkhoffian systems is studied. A reasonable form of linear autonomous Birkhoff equations is given. By combining them with the undetermined tensor method, a necessary and sufficient condition for an autonomous system to have a representation in terms of linear autonomous Birkhoff equations is obtained. The methods of constructing Birkhoffian dynamical functions are given. Two examples are given to illustrate the application of the results. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
[en] It is shown that in certain local relativistic field theories known to possess strong global solutions, time averages are not equal to the microcanonical averages computed with the Gibbs measure
[en] In a paper dedicated to unifying martingales and ergodic averages, Kachurovskii introduced certain unifying discrete-time martingale ergodic and ergodic martingale processes, for which he proved convergence theorems and established maximal and dominant inequalities. Our purpose in this article is to obtain similar results for such processes with continuous time. In addition, the results are used to assert convergence of yet another unifying process relating to Rota's approach to unification of martingales and Abel ergodic averages. Bibliography: 13 titles.
[en] A non-associative analogue of the Banach principle is developed for measurable elements with respect to a JBW-algebra. On the basis of it an individual ergodic theorem is proved for subsequences generated by means of uniform sequences
[en] Necessary and sufficient conditions are proved for ergodicity of interacting particle systems with transition functions of a relatively simple form, in both discrete and continuous time cases
[fr]On donne des conditions necessaires et suffisantes d'ergodicite de certains systemes de particules en interaction, en temps discret et temps continu, les fonctions de transition ayant une certaine forme
[en] Automorphisms on the irrational rotation algebra with respect to their ergodic properties are studied. Especially it is shown that for a dense set of the rotation parameter θ cat maps are entropic K systems. (Author)
[en] We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff’s ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.