I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 2, PAGES 357-377
On two-dimensional integral varieties of a class of discontinuous
V. F. Borisov
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We consider the following discontinuous Hamiltonian system
Here is the
Under general assumptions, we prove that a vicinity of
a singular extremal of order () contains
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).
H(y) = H0(y)+u H1(y),
u = sgn H1(y), I =
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Last modified: September 1, 2000