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Fundamentalnaya i Prikladnaya Matematika, 2000, Volume 6, Issue 2, Pages 357–377 (Mi fpm475)  

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
Bibliographic databases:
UDC: 517.977
Language: Russian
Citation: V. F. Borisov, “On two-dimensional integral varieties of a class of discontinuous Hamiltonian systems”, Fundam. Prikl. Mat., 6:2 (2000), 357–377
Citation in format AMSBIB
\Bibitem{Bor00}
\by V.~F.~Borisov
\paper On two-dimensional integral varieties of a~class of discontinuous Hamiltonian systems
\jour Fundam. Prikl. Mat.
\yr 2000
\vol 6
\issue 2
\pages 357--377
\mathnet{http://mi.mathnet.ru/fpm475}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1798189}
\zmath{https://zbmath.org/?q=an:0980.49001}
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    Фундаментальная и прикладная математика
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