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Record 1,  Textual support,  English

Record number: 1, Textual support number: 1 CONT

... a new type of bifurcation occurs in higher dimensions, namely the Hopf bifurcation. This bifurcation occurs when the derivative at a fixed point is a rotation, i.e., the multipliers are complex of modulus one.  2, record 1, English, - Hopf%20bifurcation

Record number: 1, Textual support number: 2 CONT

... Hopf bifurcation, i. e. the fixed point becomes unstable and gives birth to an invariant circle which is attractive.  3, record 1, English, - Hopf%20bifurcation

Record 1,  Textual support,  French

Record number: 1, Textual support number: 1 DEF

Bifurcation qui apparaît lorsqu'un point donne naissance à une cycle limite par franchissement d'une valeur critique.  2, record 1, French, - bifurcation%20de%20Hopf

Record number: 1, Textual support number: 1 OBS

Arnold préfère appeler cette bifurcation, bifurcation de Poincaré-Andronov. Nous nous en tiendrons à la terminologie de bifurcation de Hopf, qui est plus courante dans la littérature occidentale.  2, record 1, French, - bifurcation%20de%20Hopf

Record 1,  Textual support,  Spanish

Record 2,  Textual support,  English

Record number: 2, Textual support number: 1 DEF

A computer-based method using an underlying lattice for deciding whether two or more attractive fixed points belong to the same basin of attraction or to different basins. One could also test a basin of attraction(of an attractive or parabolic point) versus a Siegel disk, or versus a Herman ring, or even versus a divergent set(having repelling fixed points).  2, record 2, English, - boundary%20scanning%20method

Record 2,  Textual support,  French

Record number: 2, Textual support number: 1 DEF

Méthode de balayage infographique qui sert à déterminer l'appartenance de deux points fixes au même bassin d'attraction.  1, record 2, French, - m%C3%A9thode%20de%20balayage%20du%20front

Record 2,  Textual support,  Spanish

Record 3,  Textual support,  English

Record number: 3, Textual support number: 1 CONT

Neutral or indifferent periodic points come in two distinct varieties : rationally indifferent points and irrational rotations.  3, record 3, English, - indifferent%20point

Record number: 3, Textual support number: 2 CONT

Beside attractive periodic points and repelling periodic points, we may ask about indifferent points. There are two types of indifferent points : the fixed point 0 is called rationally indifferent if alpha is a rational number; it is called irrationally indifferent if alpha is an irrational number. A rationally indifferent fixed point(or cycle) is also called parabolic.  1, record 3, English, - indifferent%20point

Record number: 3, Textual support number: 1 OBS

See fixed point, periodic point, parabolic point.  4, record 3, English, - indifferent%20point

Record 3,  Textual support,  French

Record 3,  Textual support,  Spanish