Nonlinear Dynamics ( IF 5.2 ) Pub Date : 2020-11-02 , DOI: 10.1007/s11071-020-06036-0 Ognyan Christov
We study the integrability of the Hamiltonian normal form of 1:2:2 resonance. It is known that this normal form truncated to order three is integrable. The truncated to order four normal form contains many parameters. For a generic choice of parameters in the normal form up to order four, we carry on non-integrability analysis, based on the Morales–Ramis theory using only first variational equations along certain particular solutions. The non-integrability obtained by algebraic proofs produces dynamics illustrated by some numerical experiments.We also isolate a non-trivial case of integrability.
中文翻译:
关于哈密顿1:2:2共振的可积性
我们研究了1:2:2共振哈密顿正态形式的可积性。众所周知,这种截断为三阶的范式是可积的。被截断的四阶范式包含许多参数。对于一般形式的参数(最多四阶),我们基于莫拉莱斯-拉米斯理论,仅使用某些特定解的一阶变分方程,进行非可积性分析。通过代数证明获得的非可积性产生了一些数值实验说明的动力学。我们还分离出了一个非平凡的可积性案例。