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Strange attractor in the unfolding of an inclination-flip homoclinic orbit
Ergodic Theory and Dynamical Systems, 1996AbstractWe study the unfolding of a smooth vector-fieldXon ℝ3having a homoclinic orbit to a hyperbolic equilibrium point with three real eigenvalues satisfying − λss< λs< 0 < λuWe say that Γ is an inclination-flip homoclinic orbit if the extended unstable manifold at the equilibrium point is, along Γ, non-transverse to the stable manifold and ...
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Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips
Science in China Series A, 2005Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the
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Non-resonance 3D homoclinic bifurcation with an inclination flip
Chaos, Solitons and Fractals, 2009Qiuying Lu
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Homoclinic flip bifurcation with a nonhyperbolic equilibrium
Nonlinear Dynamics, 2011Xingbo Liu, Dongmei Zhang, Liu Xingbo
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Cascades of Global Bifurcations and Chaos near a Homoclinic Flip Bifurcation: A Case Study
SIAM Journal on Applied Dynamical Systems, 2018Andrus Giraldo +2 more
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Codimension-4 resonant homoclinic bifurcations with orbit flips and inclination flips
Acta Mathematica Sinica, English Series, 2015exaly