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Record 1,  Textual support,  English

Record number: 1, 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 1, English, - hyperbolicity

Record 1,  Textual support,  French

Record number: 1, 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 1, French, - hyperbolicit%C3%A9

Record number: 1, 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 1, French, - hyperbolicit%C3%A9

Record number: 1, Textual support number: 1 PHR

hyperbolicité équilatère.  2, record 1, French, - hyperbolicit%C3%A9

Record 1,  Textual support,  Spanish

Record 2,  Textual support,  English

Record number: 2, Textual support number: 1 CONT

Thus a map near a hyperbolic fixed point is always locally topologically conjugate to its derivative.  1, record 2, English, - hyperbolic%20fixed%20point

Record number: 2, 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 2, English, - hyperbolic%20fixed%20point

Record 2,  Textual support,  French

Record number: 2, Textual support number: 1 OBS

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

Record 2,  Textual support,  Spanish