Computing the Maslov index from singularities of a matrix Riccati equation

2015/10/13 by Thomas McCauley, McCauley, Thomas · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DS #math.SG

paper · pdf · doi:10.48550/arxiv.1510.03736

18 pages

arxiv created 2015/10/27 · arxiv updated 2015/10/28

Abstract

We study the Maslov index as a tool to analyze stability of steady state solutions to a reaction-diffusion equation in one spatial dimension. We show that the path of unstable subspaces associated to this equation is governed by a matrix Riccati equation whose solution S develops singularities when changes in the Maslov index occur. Our main result proves that at these singularities the change in Maslov index equals the number of eigenvalues of S that increase to +∞ minus the number of eigenvalues that decrease to -∞.

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• On the classification of Jacobi curves and their conformal curvatures

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