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On the Morse index of Lagrangian systems

✍ Scribed by Alberto Abbondandolo

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
164 KB
Volume
53
Category
Article
ISSN
0362-546X

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✦ Synopsis

We give a new proof of the identity between the Morse index of a periodic solution of a Lagrangian system, positive deΓΏnite in the velocities, and its Maslov index. Furthermore, we give an interpretation of the Maslov index when the Lagrangian system is not positive deΓΏnite in the velocities. Our approach consists in relating the Morse index of the solution to a relative Morse index obtained passing to the Hamiltonian formulation. The main concepts used are the notion of commensurable subspaces, relative dimension, Fredholm pairs and relative index of strongly indeΓΏnite bilinear forms.

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