Un indice di Morse medio per misure invarianti rispetto al flusso lagrangiano

Abbondandolo, Alberto

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 5 (1994) no. 3, pp. 213-221

Résumé

We deal with autonomous and periodic Lagrangian systems on manifolds and we introduce a mean index for invariant measures, which generalizes the mean index for periodic solutions. If the configuration space is a compact manifold with finite foundamental group, we prove that the set of mean indexes of periodic orbits is dense in \( \mathbb{R}^{+} \). If the system is periodic, we see that there exist particular sequences of periodic orbits which converge to invariant measures with a fixed mean index.