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Number 6, December 2002
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S Kh Aranson and E V Zhuzhoma
M E Changa
A S Demidov
N E Dobrinskaya
I A Dynnikov and S V Smirnov
P V Gapeev
A Giambruno and M V Zaitsev
A A Goldaeva
M M Grinenko
V N Karpushkin
V L Kurakin and A A Nechaev
R V Mikhailov
O I Mokhov
F M Mukhamedov
Yu V Muranov and D Repovs
M E Perez, G A Chechkin and E I Yablokova
A P Shashkin
N I Chernov, J L Lebowitz and Yakov G Sinai
This survey is a study of a dynamical system consisting of a massive piston in a cubic container of large size filled with an ideal gas. The piston has mass and undergoes elastic collisions with non-interacting gas particles of mass . It is found that under suitable initial conditions there is a scaling regime with time and space scaled by in which the motion of the piston and the one-particle distribution of the gas satisfy autonomous coupled equations (hydrodynamic equations) such that in the limit the mechanical trajectory of the piston converges in probability to the solution of the hydrodynamic equations for a certain period of time. There is also a heuristic discussion of the dynamics of the system on longer intervals of time.
A V Odesskii
This survey is devoted to associative -graded algebras presented by generators and quadratic relations and satisfying the so-called Poincaré-Birkhoff-Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations.
Romen V Plykin
This paper consists of two parts. The first, which is devoted to presenting results of Barge and Watkins, connects the closure of the union of the unstable manifolds of certain "Smale horseshoes" with Knaster continua and projections on them of Vietoris-van Dantzig solenoids. In the second part the homeomorphism problem for expanding attractors of codimension 1 is solved when the dimension of the manifold generating the dynamical system is greater than two.
