Spectral flow, Brouwer degree and Hill's determinant formula

Autor:	Portaluri, Alessandro, Wu, Li
Rok vydání:	2020
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Dynamical Systems Mathematics - Functional Analysis 58J30 47H11 55M25 58J20
Druh dokumentu:	Working Paper
Popis:	In 2005 a new topological invariant defined in terms of the Brouwer degree of a determinant map, was introduced by Musso, Pejsachowicz and the first name author for counting the conjugate points along a semi-Riemannian geodesic. This invariant was defined in terms of a suspension of a complexified family of linear second order Dirichlet boundary value problems. In this paper, starting from this result, we generalize this invariant to a general self-adjoint Morse-Sturm system and we prove a new spectral flow formula. Finally we discuss the relation between this spectral flow formula and the Hill's determinant formula and we apply this invariant for detecting instability of periodic orbits of a Hamiltonian system. Comment: 27 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.00956 Zobrazit plný text záznamu View this record from Arxiv