FUNDAMENTALNAYA 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 Hamiltonian systems

V. F. Borisov

Abstract

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We consider the following discontinuous Hamiltonian system

.
y
 
 = I grad H(y),
H(y) = H0(y)+u H1(y),    u = sgn H1(y),   I = æ
ç
è
0
-E
E
0
 ö
÷.
ø
Here E is the unit (n ´ n)-matrix, y Î R2n. 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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Last modified: September 1, 2000