Let $ A(t) $ be a continuous path of self-adjoint Fredholm operators, we derive 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.
Citation: Xijun Hu, Li Wu. Decomposition of spectral flow and Bott-type iteration formula[J]. Electronic Research Archive, 2020, 28(1): 127-148. doi: 10.3934/era.2020008
Let $ A(t) $ be a continuous path of self-adjoint Fredholm operators, we derive 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.
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