Congreso "Singularités réelles et complexes à Cargèse" en honor del 60 cumpleaños de Adam Parusinski

Celebrado en el Institut d'Études Scientifiques de Cargèse en  Córcega (Francia) entre el 29 de abril y el 3 de mayo de 2019.

Web:  https://ap60.sciencesconf.org/

Miembros del equipo que han participado:

-  Fernando SANZ SANCHEZ. Conferenciante invitado por el comité científico del congreso

   Título de la conferencia: "Alternative interlacing/Hardy-compatibility of solutions of ODEs with definable coefficients"

    Abstract: Framed in the qualitative study of the dynamics of three-dimensional real vector fields, and concerning specially the relative behavior of trajectories, there exists an heuristic principle that states that given a pair of trajectories, either they have infinite twisting (interlaced )or they reveal good finiteness properties. In this talk we present a result (obtained in collaboration with M. Matusinski and O. LeGal) that provides another manifestation of this principle, with a precise meaning of “finiteness property”, in a general context of vector fields definable in a polynomially bounded o-minimal structure. More precisely, written such a vector field as a system of ODEs of the form ?? ??=?(?,?),where?=(?1,?2),?definable of class ?1  and given solutions ?,?∶(0,?)→ℝ2 with exponentially flat contact and such that ? has the regular separation property with respect to the structure, then either ?,? are interlaced or the ring of functions of the form ?↦ℎ(?,?(?),?(?)), where ℎ is definable, is a Hardy field. Applied to analytic vector fields, this result refines the alternative interlacing/separation by a projection, established by Cano, Moussu and Sanz, for certain integral pencils of non-oscillating trajectories. Notably, those pencils with transcendental formal axis.

  - Jesús Alberto PALMA MARQUEZ. 

       Póster presentado: "Global monomialization of generalized analytic functions. Dimension 3"