Generalized Maslov Indices for Non-Hamiltonian Systems

We extend the definition of Maslov index to a broad class non-Hamiltonian dynamical systems. To do this, we introduce family topological spaces--which call Maslov-Arnold spaces--that share key features with Lagrangian Grassmannian, and hence admit similar theory. This contains much more. construct examples, called hyperplane spaces, that are dense in larger than Grassmannian (which is submanifold positive codimension). The resulting then used study eigenvalue problems for non-symmetric reaction-diffusion A highlight our analysis interpretation Turing instability: bifurcation occurs as one increases ratio diffusion coefficients corresponds change generalized index.