TY - JOUR
T1 - Exponentially small splitting
T2 - A direct approach
AU - Wang, Qiudong
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/6/15
Y1 - 2020/6/15
N2 - In this paper, we go beyond what was proposed in theory by Melnikov ([15]) to introduce a practical method to calculate the high order splitting distances of stable and unstable manifold in time-periodic equations. Not only we derive integral formula for splitting distances of all orders, but also we develop an analytic theory to evaluate the acquired multiple integrals. We reveal that the dominance of the exponentially small Poincaré/Melnikov function for equations of high frequency perturbation is caused by a certain symmetry embedded in the kernel functions of high order Melnikov integrals. This symmetry is beheld by many non-Hamiltonian equations.
AB - In this paper, we go beyond what was proposed in theory by Melnikov ([15]) to introduce a practical method to calculate the high order splitting distances of stable and unstable manifold in time-periodic equations. Not only we derive integral formula for splitting distances of all orders, but also we develop an analytic theory to evaluate the acquired multiple integrals. We reveal that the dominance of the exponentially small Poincaré/Melnikov function for equations of high frequency perturbation is caused by a certain symmetry embedded in the kernel functions of high order Melnikov integrals. This symmetry is beheld by many non-Hamiltonian equations.
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U2 - 10.1016/j.jde.2019.12.028
DO - 10.1016/j.jde.2019.12.028
M3 - Article
AN - SCOPUS:85077717364
SN - 0022-0396
VL - 269
SP - 954
EP - 1036
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -