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

2022/12/07 by Gonchenko, Sergey, Li, Dongchen, Turaev, Dmitry
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.03964

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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