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arXiv · 2212.03964

Universal bifurcation patterns in the unfolding of a pair of homoclinic tangencies

Sergey Gonchenko·Dongchen Li·Dmitry Turaev
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Abstract

We study generic two- and three-parameter unfoldings of a pair of orbits of quadratic homoclinic tangency in strongly dissipative systems. We prove that the corresponding stability windows for periodic orbits have various universal forms: the so-called "shrimps" (cross-road areas), as well as spring and saddle areas, and (in three-parameter unfoldings) "pregnant shrimps" (specific types of transitions between the shrimps and spring or saddle areas).

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Sergey Gonchenko, Dongchen Li, Dmitry Turaev. 2022-12-07. Universal bifurcation patterns in the unfolding of a pair of homoclinic tangencies. https://arxiv.org/abs/2212.03964

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