Two-frequency perturbation of a smooth Hamiltonian system

被引:4
|
作者
Vecheslavov, VV [1 ]
机构
[1] Russian Acad Sci, Budker Inst Nucl Phys, Siberian Div, Novosibirsk 630090, Russia
关键词
D O I
10.1134/1.1611891
中图分类号
O59 [应用物理学];
学科分类号
摘要
This work elaborates upon previous studies on the family of smooth continuous and discontinuous two-parameter Hamiltonian systems with a piecewise linear force. For such systems, the Melnikov-Arnold integral is found to be a power and oscillatory function of frequency. In the presence of two primary forcing frequencies, the secondary harmonic with a frequency that is the sum of the primary frequencies may make a major contribution to the formation of a chaotic layer. For the corresponding smooth map, the perturbation parameter ranges where, under strong local chaos, the upper separatrix of fractional resonances is retained while the lower breaks (and vice versa) are determined. It is shown that the zero angle of intersection of the separatrix branches at the central homoclinic point is not a sufficient condition for separatrix retention. Under dynamic conditions, smooth and analytical systems behave in a very different manner. (C) 2003 MAIK "Nauka / Interperiodica".
引用
收藏
页码:1079 / 1089
页数:11
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