TERMIUM Plus^®

Record 1,  Textual support,  English

Record number: 1, Textual support number: 1 CONT

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

Record number: 1, Textual support number: 1 OBS

Contrast with heteroclinic point.  3, record 1, English, - homoclinic%20point

Record number: 1, Textual support number: 2 OBS

Degenerate homoclinic point, nondegenerate homoclinic point, transverse homoclinic point.  3, record 1, English, - homoclinic%20point

Record 1,  Textual support,  French

Record 1,  Textual support,  Spanish

Record 2,  Textual support,  English

Record number: 2, Textual support number: 1 CONT

Stable manifolds of different fixed points cannot intersect owing to the property of uniqueness of trajectories passing through a given point in phase space since the crossing point would have two possible futures. The same holds for unstable manifolds of different fixed points(use the time-reversed system). In contrast, stable and unstable manifolds of different fixed points can intersect each other along special sets of trajectories called heteroclinic trajectories.  1, record 2, English, - heteroclinic%20trajectory

Record number: 2, Textual support number: 1 OBS

Such trajectories come asymptotically from one fixed point along its unstable manifold and reach asymptotically the other along its stable manifold.  1, record 2, English, - heteroclinic%20trajectory

Record 2,  Textual support,  French

Record number: 2, Textual support number: 1 CONT

Les variétés stables des différents points fixes n'ont pas le droit de se couper en raison de la propriété d'unicité des trajectoires passant par un point de l'espace des phases car le point d'intersection aurait alors deux futurs différents; de même pour des variétés instables (utiliser le renversement du sens du temps). Par contre les variétés stables et instables de différents points fixes peuvent se couper formant des ensembles particuliers de trajectoires appelées hétéroclines.  1, record 2, French, - trajectoire%20h%C3%A9t%C3%A9rocline

Record number: 2, Textual support number: 1 OBS

De telles trajectoires émergent asymptotiquement d'un point fixe le long de sa variété instable et rejoignent l'autre le long de sa variété stable.  1, record 2, French, - trajectoire%20h%C3%A9t%C3%A9rocline

Record 2,  Textual support,  Spanish

Record 3,  Textual support,  English

Record number: 3, Textual support number: 1 OBS

Contrast with homoclinic point.  2, record 3, English, - heteroclinic%20point

Record number: 3, Textual support number: 2 OBS

Degenerate heteroclinic point, nondegenerate heteroclinic point, transverse heteroclinic point.  2, record 3, English, - heteroclinic%20point

Record 3,  Textual support,  French

Record 3,  Textual support,  Spanish

Record 4,  Textual support,  English

Record number: 4, Textual support number: 1 OBS

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, record 4, English, - transverse%20heteroclinic%20point

Record 4,  Textual support,  French

Record 4,  Textual support,  Spanish

Record 5,  Textual support,  English

Record number: 5, Textual support number: 1 OBS

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, record 5, English, - transverse%20homoclinic%20point

Record 5,  Textual support,  French

Record 5,  Textual support,  Spanish