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pro vyhledávání: '"Sevryuk, Mikhail B."'
Autor:
Sevryuk, Mikhail B.
Publikováno v:
SIGMA 18 (2022), 084, 13 pages
We present three explicit curious simple examples in the theory of dynamical systems. The first one is an example of two analytic diffeomorphisms $R$, $S$ of a closed two-dimensional annulus that possess the intersection property but their compositio
Externí odkaz:
http://arxiv.org/abs/2209.02620
Autor:
Sevryuk, Mikhail B.
For various values of n, d, and the phase space dimension, we construct simple examples of Hamiltonian and reversible systems possessing smooth d-parameter families of invariant n-tori carrying conditionally periodic motions. In the Hamiltonian case,
Externí odkaz:
http://arxiv.org/abs/2005.04616
Autor:
Akimov, Vyacheslav M., Azriel, Vladimir M., Kolesnikova, Lyubov I., Rusin, Lev Yu., Sevryuk, Mikhail B.
Publikováno v:
Rendiconti Lincei. Scienze Fisiche e Naturali, 2019, Vol. 30, No. 4, pp. 785-795
We propose a general impulsive model for scattering of molecules from a flat solid surface. It is assumed within the framework of this model that an encounter of an atom (or ion) with the surface is a series of elastic (in the direction normal to the
Externí odkaz:
http://arxiv.org/abs/1910.10014
Autor:
Sevryuk, Mikhail B.
Publikováno v:
Arnold Mathematical Journal, 2018, Vol. 4, No. 3-4, pp. 415-422
It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian system (wi
Externí odkaz:
http://arxiv.org/abs/1808.03596
Autor:
Sevryuk, Mikhail B.
Publikováno v:
Regular and Chaotic Dynamics, 2017, Vol. 22, No. 6, pp. 603-615
The purpose of this brief note is twofold. First, we summarize in a very concise form the principal information on Whitney smooth families of quasi-periodic invariant tori in various contexts of KAM theory. Our second goal is to attract (via an infor
Externí odkaz:
http://arxiv.org/abs/1709.04373
Autor:
Sevryuk, Mikhail B.
Publikováno v:
The Russian version: Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), 2017, v. 63, no. 3, pp. 516-541
We consider the persistence of smooth families of invariant tori in the reversible context 2 of KAM theory under various weak nondegeneracy conditions via Herman's method. The reversible KAM context 2 refers to the situation where the dimension of th
Externí odkaz:
http://arxiv.org/abs/1709.02333
Autor:
Sevryuk, Mikhail B.
Publikováno v:
Moscow Math. J., 2017, v. 17, N 4, pp. 803-823
We revisit non-autonomous systems depending quasi-periodically in time within the reversible context 2 of KAM theory and obtain Whitney smooth families of invariant tori in such systems via Herman's method. The reversible KAM context 2 refers to the
Externí odkaz:
http://arxiv.org/abs/1612.07653
Autor:
Sevryuk, Mikhail B.
Publikováno v:
Regular and Chaotic Dynamics, 2016, Vol. 21, No. 6, pp. 599-620
We prove a general theorem on the persistence of Whitney infinitely smooth families of invariant tori in the reversible context 2 of KAM theory. This context refers to the situation where dim Fix G < (codim T)/2 where Fix G is the fixed point manifol
Externí odkaz:
http://arxiv.org/abs/1605.02586
Publikováno v:
Regular and Chaotic Dynamics, 2014, Vol. 19, No. 3, pp. 318-347
In some previous articles, we defined several partitions of the total kinetic energy T of a system of N classical particles in the d-dimensional Euclidean space into components corresponding to various modes of motion. In the present paper, we propos
Externí odkaz:
http://arxiv.org/abs/1301.3040