Asymptotic Poincaré Maps along the edges of Polytopes and their Hamiltonian character
Expositor: Hassan Alishah
Data e Horário: 11/05/18 | 14:00h
RESUMO: In this talk, I will start by describing a linear flow which encapsulates the asymptotic dynamics of flows on polytopes along the heteroclinic network formed by polytope's edges. Using this method informations such as detection of chaotic behavior and existence of normally hyperbolic stable and unstable manifolds associated to heteroclinic cycles along the polytope's edges can be obtained. In the second part, I will introduce the polymatrix replicator systems which contains several important models in Evolutionary Game Theory. Studying these systems were the main motivation for this work. I will also talk about the Hamiltonian character of these systems which will include subjects in Poisson reduction, linear Dirac structures and linear big-isotropic structures. At the end, it will be shown that in the case of Hamiltonian Polymatrix games, the linear flow encapsulating the asymptotic dynamic inherits the Hamiltonian character of the Polymatrix game. I will illustrate the results with an example. This is a joint work with Pedro Duarte and Telmo Peixe From Lisbon University.