Energia cinética e pontos de equilíbrio de sistemas hamiltonianos / Kinetic energy and equilibrium points of Hamiltonian systems

AUTOR(ES)
FONTE

IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia

DATA DE PUBLICAÇÃO

03/06/2008

RESUMO

We study a non trivial influence of the kinetic energy on equilibrium points of Hamiltonian systems following the second part of Garcia &Tal article \"The influence of the kinetic energy in equilibrium of Hamiltonian systems\". In this article the authors show, for an explicit example of C (R4 ) Hamiltonians defined by Hi = Ti + for i {1, 2}, that the attraction basins of H1 and H2 have distinct dimensions as submanifolds of R4. Well discuss how this result is related to the study of the stability according to Liapunov of equilibrium points of Hamiltonian systems and especially how it is related to the inversion of the celebrated Lagrange-Dirichlet theorem. Finally well prove a new theorem which extends the result above for a whole family of potential energies ,,k. We show that, if the parameters ,,k satisfy a simple arithmetical criteria then the attraction basins of Hi = Ti + ,,k have different dimensions for i {1, 2}.

ASSUNTO(S)

attraction basin bacia de atração energia cinética hamiltonian systems kinetic energy sistemas hamiltonianos

ACESSO AO ARTIGO

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