FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 2, PAGES 357-377
V. F. Borisov
Abstract
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We consider the following discontinuous Hamiltonian system
\begin{gather*}
\dot y = I \mathop{grad} H(y), \\
H(y)= H_0(y)+u H_1(y), \quad u = \mathop{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).
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Last modified: September 1, 2000