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Multi-dimensional Cartan prolongation and special k-flags

Piotr Mormul (2004)

Banach Center Publications

Since the mid-nineties it has gradually become understood that the Cartan prolongation of rank 2 distributions is a key operation leading locally, when applied many times, to all so-called Goursat distributions. That is those, whose derived flag of consecutive Lie squares is a 1-flag (growing in ranks always by 1). We first observe that successive generalized Cartan prolongations (gCp) of rank k + 1 distributions lead locally to all special k-flags: rank k + 1 distributions D with the derived...

Multiple periodic solutions for Hamiltonian systems with singular potential

Addolorata Salvatore (1992)

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

In this Note we prove the existence of infinitely many periodic solutions of prescribed period for a Hamiltonian system with a singular potential.

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