In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general criterion for the linear instability of a maybe degenerate) periodic orbit admitting a orbit cylinder in terms to the parity of a suitable spectral index encoding the functional and symplectic property of the problem.
- Pub Date:
- September 2021
- Mathematics - Dynamical Systems;
- Mathematics - Classical Analysis and ODEs;
- 33 pages, no figure. Comments are welcome! arXiv admin note: substantial text overlap with arXiv:1907.05864