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... the existence of a homoclinic point often implies the existence of a hyperbolic invariant set on which the map is chaotic.  2, fiche 1, Anglais, - homoclinic%20point

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Contrast with heteroclinic point.  3, fiche 1, Anglais, - homoclinic%20point

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Degenerate homoclinic point, nondegenerate homoclinic point, transverse homoclinic point.  3, fiche 1, Anglais, - homoclinic%20point

Fiche 1,  Justifications,  Français

Fiche 1,  Justifications,  Espagnol

Fiche 2,  Justifications,  Anglais

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In the same way, nothing forbids the existence of a homoclinic trajectory that starts from a fixed point along its unstable manifold and comes back to the same fixed point along its stable manifold.... The positions of the stable and unstable manifolds thus put severe constraints on the global aspect of the phase portrait of the system.  1, fiche 2, Anglais, - homoclinic%20trajectory

Fiche 2,  Justifications,  Français

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De la même façon, rien n'empêche l'existence de trajectoires homoclines partant d'un point fixe le long de sa variété instable et y retournant le long de sa variété stable [...] La position des variétés stables et instables place des contraintes sévères sur l'aspect global du portrait en phases d'un système.  1, fiche 2, Français, - trajectoire%20homocline

Fiche 2,  Justifications,  Espagnol

Fiche 3,  Justifications,  Anglais

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Contrast with homoclinic point.  2, fiche 3, Anglais, - heteroclinic%20point

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Degenerate heteroclinic point, nondegenerate heteroclinic point, transverse heteroclinic point.  2, fiche 3, Anglais, - heteroclinic%20point

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Fiche 4,  Justifications,  Anglais

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... as a family of dynamical systems develops a homoclinic point, the family undergoes a remarkably complicated sequence of bifurcations known collectively as a homoclinic bifurcation.  1, fiche 4, Anglais, - homoclinic%20bifurcation

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Fiche 5,  Justifications,  Anglais

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A homoclinic point, together with its backward orbit... and its(finite) forward orbit, is called a homoclinic orbit.  1, fiche 5, Anglais, - homoclinic%20orbit

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Degenerate homoclinic orbit, nondegenerate homoclinic orbit.  2, fiche 5, Anglais, - homoclinic%20orbit

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Fiche 5,  Justifications,  Espagnol

Fiche 6,  Justifications,  Anglais

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A homoclinic or heteroclinic point is called transverse if the respective stable and unstable manifolds meet at an angle, i. e., their tangent vectors are not collinear at the heteroclinic point.  1, fiche 6, Anglais, - transverse%20heteroclinic%20point

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Fiche 7,  Justifications,  Anglais

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A homoclinic or heteroclinic point is called transverse if the respective stable and unstable manifolds meet at an angle, i. e., their tangent vectors are not collinear at the heteroclinic point.  1, fiche 7, Anglais, - transverse%20homoclinic%20point

Fiche 7,  Justifications,  Français

Fiche 7,  Justifications,  Espagnol