Computation of the Maslov index and the spectral flow via partial signatures |
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Authors: | Roberto Giambò Paolo Piccione Alessandro Portaluri |
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Institution: | 1. Dipartimento di Matematica e Informatica, Università di Camerino, 62032 Camerino, MC, Italy;2. Departamento de Matemática, Instituto de Matemática e Estat??stica, Universidade de São Paulo, Rua do Matão 1010, CEP 05508-900, São Paulo, SP, Brazil |
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Abstract: | Given a smooth Lagrangian path, both in the finite and in the infinite dimensional (Fredholm) case, we introduce the notion of partial signatures at each isolated intersection of the path with the Maslov cycle. For real-analytic paths, we give a formula for the computation of the Maslov index using the partial signatures; a similar formula holds for the spectral flow of real-analytic paths of Fredholm self-adjoint operators on real separable Hilbert spaces. As applications of the theory, we obtain a semi-Riemannian version of the Morse index theorem for geodesics with possibly conjugate endpoints, and we prove a bifurcation result at conjugate points along semi-Riemannian geodesics. To cite this article: R. Giambò et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). |
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