On the Morse index of Lagrangian systems.
type: Item
instance of: scholarly article
title: On the Morse index of Lagrangian systems.
zbMATH Open document ID: 1082.37060
DOI: 10.1016/S0362-546X(02)00317-6
author: Alberto Abbondandolo
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-04-27T00:00:00Z
review text: We give a new proof of the identity between the Morse index of a periodic solution of a Lagrangian system, positive definite in the velocities, and its Maslov index. Furthermore, we give an interpretation of the Maslov index when the Lagrangian system is not positive definite 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 indefinite bilinear forms.
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 1900949
zbMATH Keywords: Maslov index
zbMATH Keywords: periodic solution of Lagrangian system
zbMATH Keywords: relative Morse index
zbMATH Keywords: Fredholm pairs
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1900949