Generalized Maslov indices for non-Hamiltonian systems

Autor:	Baird, Thomas John, Cornwell, Paul, Cox, Graham, Jones, Christopher, Marangell, Robert
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems Mathematics - Algebraic Topology Mathematics - Classical Analysis and ODEs Mathematics - Symplectic Geometry
Druh dokumentu:	Working Paper
Popis:	We extend the definition of the Maslov index to a broad class of non-Hamiltonian dynamical systems. To do this, we introduce a family of topological spaces--which we call Maslov-Arnold spaces--that share key topological features with the Lagrangian Grassmannian, and hence admit a similar index theory. This family contains the Lagrangian Grassmannian, and much more. We construct a family of examples, called hyperplane Maslov-Arnold spaces, that are dense in the Grassmannian, and hence are much larger than the Lagrangian Grassmannian (which is a submanifold of positive codimension). The resulting index is then used to study eigenvalue problems for non-symmetric reaction-diffusion systems. A highlight of our analysis is a topological interpretation of the Turing instability: the bifurcation that occurs as one increases the ratio of diffusion coefficients corresponds to a change in the generalized Maslov index. Comment: 50 pages, 9 figures; comments welcome! Applications in Sections 4 &5 have been significantly improved in v2
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.14517 Zobrazit plný text záznamu View this record from Arxiv