FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 2, PAGES 357377
On twodimensional integral varieties of a class of discontinuous
Hamiltonian systems
V. F. Borisov
Abstract
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We consider the following discontinuous Hamiltonian system


H(y) = H_{0}(y)+u H_{1}(y),
u = sgn H_{1}(y), I = 
æ ç
è


ö ÷.
ø






Here $E$ is the
unit $(n$´ n)matrix,
$y$Î
R^{2n}.
Under general assumptions, we prove that a vicinity of
a singular extremal of order $q$ ($2$£ q £ 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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published in Russian.
Location: http://mech.math.msu.su/~fpm/eng/k00/k002/k00202h.htm
Last modified: September 1, 2000