Oscillatory escape in a Duffing equation with a polynomial potential

[摘要] We show that the time-periodic Hamiltonian systems d(2)x/dt(2) + x(2n+1) + alpha(t) x(2l+1) = 0, 2n > 2l > n, with a discontinuity in alpha(t), possess unbounded solutions x(t) which, moreover, oscillate between a finite disk and infinity; in particular lim inf(t --> infinity) x(t) < infinity and lim sup(t --> infinity) x(t) = infinity. As a consequence, the Poincare map possesses no invariant KAM curves enclosing the origin outside a bounded disk. (C) 1997 Academic Press.

[发布日期] 1997-11-01