### Geometrical Theory of Dynamical Systems and Fluid Flows (Advanced Series in Nonlinear Dynamics)

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Classical mechanics illustrated by modern physics: Thierry Lahaye. World Scientific Lecture Notes in Physics; v. Quantum theory of the optical and electronic properties. Advanced Series in Nonlinear Dynamics; v. Introduction to digital signal processing: computer.

## Geometrical theory of dynamical systems and fluid flows / Tsutomu Kambe.

World Scientific, Angela Slavova. Series on Analysis, Applications and Computation; v. Laplace or some other matrix. Applications of this theory allowed to advance several areas of research and extract more information from real data than various other methods. It also allows to get new types of visualization of networks via building various their skeletons. Abstract: Channel flow of an incompressible fluid at Reynolds numbers above possesses a number of different spatially localized solutions which approach the laminar flow far upstream and downstream.

We use one such relative time-periodic solution that corresponds to a spatially localized version of a Tollmien-Schlichting wave to illustrate how the upstream and downstream asymptotics can be computed analytically. In particular, we show that for these spanwise uniform states the asymptotics predict exponential localization that has been observed for numerically computed solutions of several canonical shear flows but never properly understood theoretically. Talk Title: The Pageault barrier: a tool to find the recurrent part of a dynamical system. Abstract: If f is a invertible dynamical system on a compact space X.

To find these states Conley introduced an approach through chain recurrence and Lyapunov functions. The purpose of this lecture is to introduce the Pageault barrier to study these problems. This a more metric approach, meaning that we can introduce a kind of distance that allows to locate the pieces where the recurrent dynamics is occurring. Talk Title: Perturbations of quasi-periodic orbits: From Theory to computations. Abstract: Since the time if Hyparco, it was known that the motion of celestial bodies is approximately given by epicycles.

K letiyu so dnya rozhdeniya akademika Nikolaya Nikolaevicha Bogolyubova , — [Proc. Steklov Inst. Sinai, An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations , Commun. Sinai, Simple random walks on tori , J. Sinai, Mathematical problems of turbulence , Physica A , Sinai, Navier-Stokes systems with periodic boundary conditions , Regul. Sinai, Dinamika massivnoi chastitsy, okruzhennoi konechnym chislom legkikh chastits , TMF, 1 , — [Y.

Sinai, Dynamics of a heavy particle surrounded by a finite number of light particles , Theor.

## PhD Projects and Supervision

Sinai, Anomalous transport in quasi-periodic media , Russ. Sinai, A mechanism of ergodicity in standard-like maps. C, Math. Dordrecht: Kluwer Academic Publishers. Borisyuk, I. Lunin, E. Nikolaev, Yu. Radvogin, M.

## American Institute of Mathematical Sciences

Roitberg, Ya. Arnol'd, R. Borisyuk, E. Gel'fand, Yu. Il'yashenko, V. Khibnik, Emmanuil El'evich Shnol' on his 70th birthday , Russ. Galeev, E.

Kuznetsov, A. Mikhailov, Yu. Nesterikhin, C. Novikov, R. Sinai, G.

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Smirnov, V. Fortov, I. Khalatnikov, B. Chirikov, A.

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Nesterikhin, S. Shabad, Vladimir Evgen'evich Zakharov on his sixtieth birthday , Phys. Soshnikov, Central limit theorem for traces of large random symmetric matrices with independent matrix elements.

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Goldstein, J. Lebowitz, Y. Sinai, Parabolic perturbations of Hamilton-Jacobi equations. Sinai, Asymptotic behavior of solutions of 1D-Burgers equation with quasi-periodic forcing , Topol. Methods Nonlinear Anal. Soshnikov, Utochnenie polukrugovogo zakona Vignera v okrestnosti kraya spektra dlya sluchainykh simmetrichnykh matrits , Funkts. Soshnikov, A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices , Funct. Sinai, Convex hulls of random processes , Amer. Edited by: A. Varchenko and V.

Vassiliev, AMS, , pp.

Gurarii, V. Zakharov, V. Marchenko, V. Maslov, A. Pogorelov, Ya. Khruslov, Leonid Andreevich Pastur k shestidesyatiletiyu so dnya rozhdeniya , Uspekhi mat.