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Fundamentalnaya i Prikladnaya Matematika, 2000, Volume 6, Issue 2, Pages 357–377
(Mi fpm475)
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On two-dimensional integral varieties of a class of discontinuous Hamiltonian systems
V. F. Borisov State Academy of Consumer Services
Abstract:
We consider the following discontinuous Hamiltonian system
\begin{gather*}
\dot y=I\operatorname{grad}H(y),
\\
H(y)=H_0(y)+u H_1(y),\quad
u=\operatorname{sgn}H_1(y),\quad
I=\begin{pmatrix}
0 &-E
\\
E &0
\end{pmatrix}.
\end{gather*}
Here $E$ is the unit $(n\times n)$-matrix, $y\in\mathbb R^{2n}$. Under general assumptions, we prove that a vicinity of a singular extremal of order $q$ ($2\le q\le n$) contains $[q/2]$ integral varieties with chattering trajectories. That means that the trajectories enter into the singular extremal at a finite instant with an infinite number of intersections with the surface of discontinuity (Fuller's phenomenon).
Received: 01.02.1997
Citation:
V. F. Borisov, “On two-dimensional integral varieties of a class of discontinuous Hamiltonian systems”, Fundam. Prikl. Mat., 6:2 (2000), 357–377
Linking options:
https://www.mathnet.ru/eng/fpm475 https://www.mathnet.ru/eng/fpm/v6/i2/p357
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Abstract page: | 175 | Full-text PDF : | 93 | First page: | 2 |
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