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Strange attractor in the unfolding of an inclination-flip homoclinic orbit
AbstractWe 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 ...
Vincent Naudot
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On inclination-flip homoclinic orbit associated to a saddle-node singularity
The author studies the bifurcation of vector fields through a saddle-node equilibrium point with an unstable homoclinic orbit. The study is made in the setting of two parameters perturbations of the vector fields \((X_{\mu})_{\mu\in\mathbb{R}^2}\) and in the case that \(X_{(0,0)}\) exhibits an inclination-flip homoclinic orbit associated to the ...
C. A. Morales
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Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips
Homoclinic 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
Shuliang Shui
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