The problem. We have seen during the first workshop many attempts to bring the theory of dynamical systems to bear on the issue of non-equilibrium statistical mechanics. The main gap to close the circle is to learn how to treat system with many say components. This is very hard and, at the moment, can be done only in the very simple case of coupled map lattices.
A more direct approach, and more dynamical in nature, is desirable also because in the non-smooth case conjugation fails. Super-brief history of the transfer operator approach. They were able to prove spectral gap in finitely many di-mensions and existence of a measure with absolutely continuos marginals in infinite dimensions. Then Fischer, Rugh  and Rugh  managed to prove space-time decay of correlations in infinite dimensions in the analytic case.
Finally, in  it was proved the spectral gap for piecewise expanding CML. The latter paper is what I will explain in the following.
Location of Repository. Provided by: CiteSeerX. Suggested articles.We study the asymptotic statistical behavior of the 2-dimensional periodic Lorentz gas with an infinite horizon. We consider a particle moving freely in the plane with elastic reflections from a periodic set of fixed convex scatterers. We assume that the initial position of the particle in the phase space is random with uniform distribution with respect to the Liouville measure of the periodic problem.
We are interested in the asymptotic statistical behavior of the particle displacement in the plane as the time t goes to infinity. We assume that the particle horizon is infinite, which means that the length of free motion of the particle is unbounded. We find the covariance matrix of the limit distribution. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Lorentz, The motion of electrons in metallic bodies, Proc.
Google Scholar. Gallavotti, Divergences and the approach to equilibrium in the Lorentz and the wind-tree models, Phys.
Goldstein, J. Lebowitz, and M. Aizenman, Ergodic properties of infinite systems, in Lecture Notes in Physics 38 — Sinai, Ergodic properties of the Lorentz gas, Funkts. Ego Prilozh. Bunimovich and Ya.
Sinai, Markov partitions for dispersed billiards, Commun. Sinai, Statistical properties of Lorentz gas with periodic configuration of scatterers, Commun. Bunimovich, Decay of correlations in dynamical systems with chaotic behavior, Zh.
JETP 62 — Casati, G.
Comparin, and I. Guarneri, Decay of correlations in certain hyperbolic systems, Phys. A 26 — Machta, Power law decay of correlations in a billiard problem, J. Machta and R. Zwanzig, Diffusion in a periodic Lorentz gas, Phys. Friedman, Y. Oono, and I. Kubo, Universal behavior of Sinai billiard systems in the small-scatterer limit, Phys.
Friedman and R.T t is the time evolution which describes free motion of the particles except for elastic collisions with each other and with the wall at the origin.
This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Sinai, Ya. Google Scholar. Goldstein, S. In: Dynamical systems, theory, and application. Moser J. Lecture Notes in Physics, Vol. Berlin, Heidelberg, New York: Springer Landau, L. New York: Pergamon Cornfeld, I. Download references. Reprints and Permissions.Shy emoji
Boldrighini, C. Ergodic properties of a semi-infinite one-dimensional system of statistical mechanics. Download citation. Received : 05 September Issue Date : September Search SpringerLink Search. Immediate online access to all issues from Subscription will auto renew annually. Taxes to be calculated in checkout. References 1. Soloveichik Authors C.
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Properties of Infinite Dimensional Hamiltonian Systems
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Ergodic properties of a semi-infinite one-dimensional system of statistical mechanics
Properties of infinite dimensional Hamiltonian systems Paul R. Not in Library. Want to Read. Download for print-disabled. Check nearby libraries Library. Share this book Facebook. Last edited by Clean Up Bot. October 9, History. An edition of Properties of infinite dimensional Hamiltonian systems This edition published in by Springer-Verlag in Berlin.
New York. Written in English — pages. Subjects DynamicsHamiltonian systemsSemigroups. Properties of infinite dimensional Hamiltonian systemsSpringer-Verlag.Unops salary scale ics 10
Properties of infinite dimensional Hamiltonian systems First published in Subjects DynamicsHamiltonian systemsSemigroups. Edition Notes Bibliography: p.
Series Lecture notes in mathematics ;Lecture notes in mathematics Springer-Verlag ;, L28 no. The Physical Object Pagination p. Lists containing this Book.Infinite dimensions
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Properties of infinite dimensional Hamiltonian systems
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Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon
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