Chaotic Dynamics and Transport in Classical and Quantum by P. Collet (auth.), P. Collet, M. Courbage, S. Métens, A.

By P. Collet (auth.), P. Collet, M. Courbage, S. Métens, A. Neishtadt, G. Zaslavsky (eds.)

From the 18th to the thirtieth August 2003 , a NATO complex examine Institute (ASI) was once held in Cargèse, Corsica, France. Cargèse is a pleasant small village positioned by way of the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese presents ? a conventional position to prepare Theoretical Physics summer time faculties and Workshops * in a closed and good equiped position. The ASI was once a world summer season university on "Chaotic Dynamics and delivery in Classical and Quantum Systems". the most target of the college used to be to increase the mutual interplay among Physics and arithmetic relating statistical homes of classical and quantum dynamical structures. numerous experimental and numerical observations have proven new phenomena of chaotic and anomalous delivery, fractal constructions, chaos in physics accelerators and in cooled atoms within atom-optics billiards, space-time chaos, fluctuations faraway from equilibrium, quantum decoherence and so forth. New theoretical equipment were built with the intention to modelize and to appreciate those phenomena (volume conserving and ergodic dynamical structures, non-equilibrium statistical dynamics, fractional kinetics, coupled maps, space-time entropy, quantum dissipative tactics etc). the varsity accrued a staff of experts from a number of horizons lecturing and discussing at the achievements, views and open difficulties (both primary and applied).

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Chaotic Dynamics and Transport in Classical and Quantum Systems: Proceedings of the NATO Advanced Study Institute on International Summer School on Chaotic Dynamics and Transport in Classical and Quantum Systems Cargèse, Corsica 18–30 August 2003

From the 18th to the thirtieth August 2003 , a NATO complex research Institute (ASI) used to be held in Cargèse, Corsica, France. Cargèse is a pleasant small village positioned by way of the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese presents ? a conventional position to arrange Theoretical Physics summer time faculties and Workshops * in a closed and good equiped position.

Additional info for Chaotic Dynamics and Transport in Classical and Quantum Systems: Proceedings of the NATO Advanced Study Institute on International Summer School on Chaotic Dynamics and Transport in Classical and Quantum Systems Cargèse, Corsica 18–30 August 2003

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I−1 ) ∈ A0 ×· · · ×Ai−1 is maximal when ωj = qj − 1 for each j = 0, . . , i − 1. Theorem 1 is extended to polysymbolic systems as follows. Theorem 2 Let (Ωq∗ , T ) be a multipermutative system which is polysymbolic. Then the following statements are equivalent. (P1). (Ωq∗ , T ) is minimal. (P2). For every L > 0 and every cylinder ω L := [ω0 , . . , ωL−1 ] the seL−1 quence ω L , T ω L , T 2 ω L , . . is periodic with smallest period i=0 qi . (P3). For every L > 0 the numbers πL := ω pL (ω L ) and the constant L p0 ∈ A are relatively prime to qL and q0 , respectively.

We consider now multipermutative systems with different alphabets Ai = {0, . . , qi −1} at every coordinate i = 0, 1, . . Such systems will be referred to as polysymbolic systems. The set of sequences is Ωq∗ = A0 × A1 × · · · , and the size of alphabets at every coordinate i is denoted by the sequence q∗ = (q0 , q1 , . ) of positive integers qi = card(Ai ), i ≥ 0. A polysymbolic system (Ωq∗ , T ) is multipermutative if for every ω = (ω0 , ω1 , . . ) the map T : Ωq∗ → Ωq∗ is defined by T ω = (ω0 + p0 , ω1 + p1 (ω0 ), .

All these results imply the K-property. Beck and Roepstorff developped an analogous model of the Langevin equation by the convergence of such kind of random walk generated by Bernoulli DS to the Ornstein-Uhlenbeck process [1]. 31) to a finite non zero ”diffusion coefficient” σ for some ”large” class of ”smooth” functions f. Then the central limit theorem means the convergence of the normalized sums Sn1 f Sn f (x) in distribution to the reduced normal law. Such theorem does not imply necessarly mixing properties.

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