Mercoledì 15 giugno alle ore 15, in aula Seminari (III piano edificio H2bis), il dr. Eduardo Muñoz-Hernández, in visita in Italia, presenterà il seminario:

 

 

Title: Index theory for planar Hamiltonian systems with applications to the existence of subharmonics

 

Abstract: In this talk, we present a recap of the index theory for linear planar Hamiltonian systems with periodic coefficients providing the relationship between the stability of the system, the Conley-Zehnder index, the winding number of solutions and their respective asymptotic indices. Although most of these relationships are well known, we take a slightly different a priori classification in order to give a more natural definition of the Conley-Zehnder index for resonant cases from the point of view of the rotational behavior of solutions. This seems to be more appropriate to the analysis of the existence and multiplicity of subharmonics in nonlinear planar Hamiltonian systems via the Poincar\'e--Bikhoff theorem, as will be discussed in the second part of the talk. This is a joint work with Alberto Boscaggin from the University of Turin.