## DYNAMICAL SYSTEMS Seminar

### Approaching the $C^2$ Genericity of Hamiltonians Through Probabilistic Methods. Profit Maximization and Symplectic Structures

Filipe Santos
(ISEG and CEMAPRE)

Abstract: The question about the $C^2$ genericity of Hamiltonians consists in finding the existence of a $C^2$-residual set of Hamiltonians, for which, exists an open mod 0 dense set of regular energy surfaces each being either partially hyperbolic or with vanishing Lyapunov exponents almost everywhere. In this talk I establish the main concept of dominated splitting and its relation to partially hyperbolic splittings, namely, in the context of symplectic manifolds. The tools to prove the claimed genericity are briefly presented with emphasis on "dynamically guided" random walks. Finally, and since the symplectic structure plays a main role in this problem, an application of this abstract concept in economics is shown, with the derivation of Samuelsons's profit maximization criteria for a firm, solely through symplectic relations.

Friday, January 6, 2017
Time: 14h30
Room: Sala IAPMEI, Edificio Quelhas, ISEG
http://cemapre.iseg.ulisboa.pt/seminars/dynsys/