Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral flow, Brouwer degree and Hill's determinant formula   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.

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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th