Decomposition of spectral flow and Bott-type iteration formula

Xijun Hu; Li Wu; Xijun Hu; Li Wu

doi:10.3934/era.2020008

Electronic Research Archive

2020, Volume 28, Issue 1: 127-148. doi: 10.3934/era.2020008

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Decomposition of spectral flow and Bott-type iteration formula

Xijun Hu ,
Li Wu ^,

School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received: 01 September 2019 Revised: 01 January 2020
58J30, 37B30, 53D12

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.
- Spectral flow,
- cogredient invariant,
- decomposition formula,
- Bott-type iteration formula
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

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Abstract

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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