Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Zharnitsky, Vadim"'
Autor:
Lerman, Ariel, Zharnitsky, Vadim
Experimental realizations of trapping Bose Einstein condensate lead to a Hamiltonian system of a classical particle bouncing off a convex scatterer in the field of an attracting potential. It is shown by application of KAM theory that under some natu
Externí odkaz:
http://arxiv.org/abs/2104.03357
We study convergence of nonlinear systems in the presence of an `almost Lyapunov' function which, unlike the classical Lyapunov function, is allowed to be nondecreasing---and even increasing---on a nontrivial subset of the phase space. Under the assu
Externí odkaz:
http://arxiv.org/abs/1812.04474
Autor:
Wayne, C. Eugene, Zharnitsky, Vadim
We study a pair of infinite dimensional dynamical systems naturally associated with the study of minimizing/maximizing functions for the Strichartz inequalities for the Schr\"odinger equation. One system is of gradient type and the other one is a Ham
Externí odkaz:
http://arxiv.org/abs/1712.07239
A nonlinear Schr\"odinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises naturally in modeling fiber-optics communication systems with periodical
Externí odkaz:
http://arxiv.org/abs/1707.06944
Publikováno v:
In Automatica March 2020 113
Autor:
Arnold, Maxim, Zharnitsky, Vadim
A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a canonical
Externí odkaz:
http://arxiv.org/abs/1303.5510
Autor:
Merenkov, Sergei, Zharnitsky, Vadim
We prove that the Hausdorff dimension of the set of three-period orbits in classical billiards is at most one. Moreover, if the set of three-period orbits has Hausdorff dimension one, then it has a tangent line at almost every point.
Comment: 10
Comment: 10
Externí odkaz:
http://arxiv.org/abs/1112.2745
Autor:
Baryshnikov, Yuliy, Zharnitsky, Vadim
The classical linear search problem is studied from the view point of Hamiltonian dynamics. For the specific, yet representative case of exponentially distributed position of the hidden object, we show that the optimal plan follows an unstable separa
Externí odkaz:
http://arxiv.org/abs/1108.2498
An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is found that the set of 3-period orbits in billiards on hyperbolic plane, a
Externí odkaz:
http://arxiv.org/abs/1108.0987
An n-simplex is said to be n-well-centered if its circumcenter lies in its interior. We introduce several other geometric conditions and an algebraic condition that can be used to determine whether a simplex is n-well-centered. These conditions, toge
Externí odkaz:
http://arxiv.org/abs/0912.3097