Maslov Index, Spectral Flow and Bifurcation of Electromagnetic Geodesics Within an Energy Level

Abstract

We develop appropriate notions of Maslov index and spectral flow for electromagnetic geodesics within a fixed energy level and prove a Morse Index type theorem in this context. This is then applied to the problem of electromagnetic geodesics, all of whose energy are the same, bifurcating from a given one.

arXiv commentDefinition 1.1 has been corrected. Some references have been added and the Introduction has been improved. Two examples have been included as well as a new subsection (Sec. 8.6). Accepted for publication in Nonlinearity