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Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C.

Colin ChristopherChristiane Rousseau — 2001

Publicacions Matemàtiques

In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. The sufficiency of these conditions is shown by exhibiting explicitly a linearizing change of coordinates, either of Darboux type or a generalization of it.

Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle

Christiane RousseauColin Christopher — 2007

Annales de l’institut Fourier

We consider germs of one-parameter generic families of resonant analytic diffeomorphims and we give a complete modulus of analytic classification by means of the unfolding of the Écalle modulus. We describe the parametric resurgence phenomenon. We apply this to give a complete modulus of orbital analytic classification for the unfolding of a generic resonant saddle of a 2-dimensional vector field by means of the unfolding of its holonomy map. Here again the modulus is an unfolding of the Martinet-Ramis...

Skupinový screening

Christian GenestChristiane Rousseau — 2021

Pokroky matematiky, fyziky a astronomie

Skupinový screening je nezbytnou součástí boje proti šíření koronaviru. Jak ale čelit možnému nedostatku činidel a materiálu? Tím, že budeme provádět testy na bázi promíchání vzorků a využijeme přitom matematiku.

The modulus of analytic classification for the unfolding of the codimension-one flip and Hopf bifurcations

Waldo Arriagada-SilvaChristiane Rousseau — 2011

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we study equivalence classes of generic 1 -parameter germs of real analytic families 𝒬 ε unfolding codimension 1 germs of diffeomorphisms 𝒬 0 : ( , 0 ) ( , 0 ) with a fixed point at the origin and multiplier - 1 , under (weak) analytic conjugacy. These germs are generic unfoldings of the flip bifurcation. Two such germs are analytically conjugate if and only if their second iterates, 𝒫 ε = 𝒬 ε 2 , are analytically conjugate. We give a complete modulus of analytic classification: this modulus is an unfolding of the Ecalle...

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