TERMIUM Plus^®

Record 1,  Textual support,  English

Record number: 1, Textual support number: 1 DEF

Bow, similar to a rainbow, often hyperbolic in shape, formed by the refraction and reflection of the Sun’s rays in dew drops.  3, record 1, English, - dewbow

Record number: 1, Textual support number: 1 CONT

Dew bows are rainbows which form in spherical dew droplets. The bows are relatively rare; usually you only see a portion of the dewbow in a spiderweb, a wall, or on grass and vegetation. Some grasses may show the dewbow very nicely while others will not. The dewbow appears spherical around the antisolar point, but if you see it projected on the ground, the projection may look elliptical, parabolic or hyperbolic depending on solar altitude.  2, record 1, English, - dewbow

Record 1,  Textual support,  French

Record number: 1, Textual support number: 1 DEF

Arc, semblable à l'arc-en-ciel, souvent de forme hyperbolique, formé au sol par la réfraction et la réflexion des rayons du Soleil dans les gouttes de rosée.  1, record 1, French, - arc%2Den%2Dciel%20de%20ros%C3%A9e

Record number: 1, Textual support number: 1 OBS

Pluriel : arcs-en-terre.  3, record 1, French, - arc%2Den%2Dciel%20de%20ros%C3%A9e

Record 1,  Textual support,  Spanish

Record number: 1, Textual support number: 1 DEF

Arco, similar al arco iris, a menudo de forma hiperbólica, formado por la refracción y la reflexión de los rayos solares en las gotas de rocío.  1, record 1, Spanish, - arco%20del%20roc%C3%ADo

Record 2,  Textual support,  English

Record number: 2, 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 2, English, - homoclinic%20point

Record number: 2, Textual support number: 1 OBS

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

Record number: 2, Textual support number: 2 OBS

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

Record 2,  Textual support,  French

Record 2,  Textual support,  Spanish

Record 3,  Textual support,  English

Record number: 3, Textual support number: 1 CONT

To define a hyperbolic set, we first recall the situation near a hyperbolic fixed point. Basically, there were two ingredients to hyperbolicity, a rate of expansion or contraction, given by the eigenvalues of the Jacobian matrix at the point, and a direction of expansion or contraction, given by the associated eigenvector.  2, record 3, English, - hyperbolicity

Record 3,  Textual support,  French

Record number: 3, Textual support number: 1 DEF

Propriété géométrique qui implique une convergence des trajectoires dans une direction et leur divergence dans une autre direction.  2, record 3, French, - hyperbolicit%C3%A9

Record number: 3, Textual support number: 1 OBS

On la retrouve dans l'attracteur de Hénon et dans la transformation d'un cercle en ellipse, caractérisés par l'étirement des longueurs dans une direction et leur contraction dans la direction perpendiculaire.  2, record 3, French, - hyperbolicit%C3%A9

Record number: 3, Textual support number: 1 PHR

hyperbolicité équilatère.  2, record 3, French, - hyperbolicit%C3%A9

Record 3,  Textual support,  Spanish

Record 4,  Textual support,  English

Record number: 4, Textual support number: 1 CONT

Thus a map near a hyperbolic fixed point is always locally topologically conjugate to its derivative.  1, record 4, English, - hyperbolic%20fixed%20point

Record number: 4, Textual support number: 2 CONT

It is an easy exercise using the Implicit Function Theorem to show that hyperbolic fixed and periodic points must persist under small perturbation....  1, record 4, English, - hyperbolic%20fixed%20point

Record 4,  Textual support,  French

Record number: 4, Textual support number: 1 OBS

Le point fixe est stable ou instable.  2, record 4, French, - point%20fixe%20hyperbolique

Record 4,  Textual support,  Spanish