Dicotomia de Bochi-Mañé 2d-dimensional para sistemas hamiltonianos

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Bochi-Mañé dichotomy for 2n-Hamiltonians, Random Perturbation Techniques

Publication . Santos, Filipe André Paulino; Dias, João Lopes

We prove the high dimensional version of the Bochi-Mañé dichotomy for Hamiltonian systems, achieving for the fi rst time in a continuous setting such a general result. That is, we nd the existence of a C2-residual set of Hamiltonians for which there is an open mod 0 dense set of regular energy surfaces each being either Anosov or for almost every x, either LE(x) = 0 or there is a partially hyperbolic splitting . A generalization of Bochi's random perturbative technique is developed and used in the Hamiltonian framework, to show the extended reach of probabilistic methods and their importance on the nesting and iterative process of perturbations. The main technique consists in letting the original dynamics component act on the invariant subspaces while the random component acts on the direction we are iteratively perturbing. We also connect reachability properties of dynamically guided stochastic processes with the existence or lack of domination on orbits

2020Tese de doutoramento

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Fundação para a Ciência e a Tecnologia

Programa de financiamento

OE

Número da atribuição

SFRH/BD/110545/2015