Abstract
We study the resonance ω1∶ω2 = 4∶1 and some near-resonance cases. The main peculiarity of this resonance is that for ω1∶ω2 < 4 the characteristic of the central periodic orbits is broken into two and each part is joined with a resonant characteristic. This behaviour is described theoretically by means of the ‘third’ integral. It seems that there are infinite families of simple periodic orbits near the escape region. Finally, a comparison is made with the cases near the ω1∶ω2 = 2∶1 resonance.
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Contopoulos, G. The 4∶1 resonance. Celestial Mechanics 24, 355–366 (1981). https://doi.org/10.1007/BF01230395
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DOI: https://doi.org/10.1007/BF01230395