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Bifurcation of a heterodimensional cycle with weak inclination flip

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  • Local moving frame is constructed to analyze the bifurcation of a heterodimensional cycle with weak inclination flip in $\mathbb{R}^4$. Under some generic hypotheses, the existence conditions for the heteroclinic orbit, $1$-homoclinic orbit, $1$-periodic orbit and two-fold or three-fold $1$-periodic orbit are given, respectively.
    Mathematics Subject Classification: Primary: 34C23, 37G10; Secondary: 34D09.

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