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pro vyhledávání: '"Treschev A."'
Autor:
Treschev, Dmitry
Following arXiv:2303.02992, we develop an approach to the Hamiltonian theory of normal forms based on continuous averaging. We concentrate on the case of normal forms near an elliptic singular point, but unlike arXiv:2303.02992 we do not assume that
Externí odkaz:
http://arxiv.org/abs/2404.07043
Autor:
Treschev, Dmitry
We consider the Schr\"odinger equation $ih\partial_t\psi = H\psi$, $\psi=\psi(\cdot,t)\in L^2({\mathbb T})$. The operator $H = -\partial^2_x + V(x,t)$ includes smooth potential $V$, which is assumed to be time $T$-periodic. Let $W=W(t)$ be the fundam
Externí odkaz:
http://arxiv.org/abs/2404.06999
Autor:
Treschev, Dmitry
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a differenti
Externí odkaz:
http://arxiv.org/abs/2303.02992
Autor:
Treschev, Dmitry
Publikováno v:
J. Dyn. Diff. Equat. 33, 1269-1295 (2021)
In \cite{Tre_PSI20} we introduce the concept of a $\mu$-norm for a bounded operator in a Hilbert space. The main motivation is the extension of the measure entropy to the case of quantum systems. In this paper we recall the basic results from \cite{T
Externí odkaz:
http://arxiv.org/abs/2112.15078
Autor:
Treschev, Dmitry
Publikováno v:
Proc. Steklov Inst. Math., 310 (2020), 262-290
Let $({\cal X},\mu)$ be a measure space. For any measurable set $Y\subset{\cal X}$ let $1_Y : {\cal X}\to{\mathbb R}$ be the indicator of $Y$ and let $\pi_Y$ be the orthogonal projector $L^2({\cal X})\ni f\mapsto\pi_Y f = 1_Y f$. For any bounded oper
Externí odkaz:
http://arxiv.org/abs/2112.15073
Autor:
Treschev, Dmitry
Our main result is the complete set of explicit conditions necessary and sufficient for isochronicity of a Hamiltonian system with one degree of freedom. The conditions are presented in terms of Taylor coefficients of the Hamiltonian function.
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Externí odkaz:
http://arxiv.org/abs/2112.15063
Autor:
Treschev, Dmitry
Let $q:M\to M$ be a volume-preserving diffeomorphism of a smooth manifold $M$. We study the possibility to present $q$ as the Poincar\'e map, corresponding to a volume-preserving vector field on $\mathbb{T}\times M$, $\mathbb{T} = \mathbb{R}/\mathbb{
Externí odkaz:
http://arxiv.org/abs/1911.09420
Autor:
Davletshin, Mars, Treschev, Dmitry
We study the Arnold diffusion in a priori unstable near-integrable systems in a neighbourhood of a resonance of low order. We consider a non-autonomous near-integrable Hamiltonian system with $n+1/2$ degrees of freedom, $n\ge 2$. Let the Hamilton fun
Externí odkaz:
http://arxiv.org/abs/1807.07832
Autor:
Treschev, Dmitry
We consider a multi-dimensional billiard system in an (n+1)-dimensional Euclidean space, the direct product of the "horizontal" hyperplane and the "vertical" line. The hypersurface that determines the system is assumed to be smooth and symmetric in a
Externí odkaz:
http://arxiv.org/abs/1612.00187
We consider the following problem: given two parallel and identically oriented bundles of light rays in n-dimensional Euclidean space and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to r
Externí odkaz:
http://arxiv.org/abs/1602.07961