A topological approach to stability of pulses bifurcating from an inclination-flip homoclinic orbit (Q5937118)

The paper deals with the linear stability problem of multiple pulse solutions of a parabolic system, which bifurcate from an inclination-flip homoclinic orbit. A topological approach is applied to the eigenvalue problem and a relation between the distribution of the eigenvalues and the geometry of the homoclinic orbits is proven. While the description of the inclination-flip homoclinic orbit is rather clear, the remaining results are stated without sufficient explanations to understand the topological content of the paper, which could be quite important.