TY - JOUR
T1 - Oscillatory Escape in a Duffing Equation with a Polynomial Potential
AU - Levi, Mark
AU - You, Jiangong
N1 - Funding Information:
* Research partially supported by an NSF grant.
PY - 1997/11/1
Y1 - 1997/11/1
N2 - We show that the time-periodic Hamiltonian systemsd2x/dt2+x2n+1+a(t)x2l+1=0, 2n>2l>n, with a discontinuity ina(t), possess unbounded solutionsx(t) which, moreover, oscillate between a finite disk and infinity; in particular liminft→∞x(t)<∞ and limsupt→∞x(t)=∞. As a consequence, the Poincaré map possesses no invariant KAM curves enclosing the origin outside a bounded disk.
AB - We show that the time-periodic Hamiltonian systemsd2x/dt2+x2n+1+a(t)x2l+1=0, 2n>2l>n, with a discontinuity ina(t), possess unbounded solutionsx(t) which, moreover, oscillate between a finite disk and infinity; in particular liminft→∞x(t)<∞ and limsupt→∞x(t)=∞. As a consequence, the Poincaré map possesses no invariant KAM curves enclosing the origin outside a bounded disk.
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U2 - 10.1006/jdeq.1997.3305
DO - 10.1006/jdeq.1997.3305
M3 - Article
AN - SCOPUS:0000064953
SN - 0022-0396
VL - 140
SP - 415
EP - 426
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -