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.
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 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.
In this paper we study equivalence classes of generic -parameter germs of real analytic families unfolding codimension germs of diffeomorphisms with a fixed point at the origin and multiplier 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, are analytically conjugate. We give a complete modulus of analytic classification: this modulus is an unfolding of the Ecalle...
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