Decomposition of Spectral flow and Bott-type Iteration Formula

2018/08/13 by Xijun Hu, Hu, Xijun, Li Wu +1
Computer Science · Mathematics · #37B30 #53D12 #58J30 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1808.04268

openalex publication_date 2018/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A(t) be a continuous path of Fredhom operators, we first prove that the spectral flow sf(A(t)) is cogredient invariant. Based on this property, we give a decomposition formula of spectral flow if the path is invariant under a matrix-like cogredient. As applications, we give the generalized Bott-type iteration formula for linear Hamiltonian systems.

Citations

• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations

Related

• The Equivariant Spectral Flow and Bifurcation of Periodic Solutions of Hamiltonian Systems
• On spectral flow for operator algebras
• On a Comparison Principle and the Uniqueness of Spectral Flow
• Spectral flow as winding number and integral formulas
• Ordinary differential equations in Banach spaces and the spectral flow