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Variational characterization of equations of motion in bundles of embeddings.

Hernán Cendra, Ernesto A. Lacomba (1989)

Revista Matemática Iberoamericana

In this paper we study variational principles for a general situation which includes free boundary problems with surface tension. Following [2], our main result concerns a variational principle in a infinite dimensional principal bundle of embeddings of a compact region D in a manifold M having the same dimension as D. By considering arbitrary variations, free boundary problems are included, while variations parallel to the boundary permit to consider fluid motion or flow of Hamiltonian vector fields...

Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium

Massimiliano Berti, Philippe Bolle (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider autonomous Lagrangian systems possessing two homoclinic orbits to an hyperbolic equilibrium of saddle-saddle type with two different characteristic exponents. Under a nondegeneracy assumption on the homoclinics and under suitable conditions on the geometric behaviour of these homoclinics near the equilibrium we show, by variational methods, that they give rise to an infinite family of multibump homoclinic solutions. We relax the nondegeneracy assumption when the two characteristic exponents...

Vecteurs propres de matrices de Jacobi

Michèle Audin (1994)

Annales de l'institut Fourier

On montre que l’ensemble des matrices tridiagonales périodiques symétriques de spectre fixé possède une direction tangente privilégiée, construite à l’aide des vecteurs propres des matrices et de la jacobienne d’une courbe hyperelliptique. Il se trouve que cette direction est celle du célèbre flot de Toda périodique.

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