Isospectral flows on a class of finite-dimensional Jacobi matrices

Details Isospectral flows on a class of finite-dimensional Jacobi matrices Isospectral flows on a class of finite-dimensional Jacobi matrices

2012-02-08

arxiv.org/abs/1202.1618v1

Mathematics

Dynamical Systems

15 pages, 2 figures

Scientific paper

We present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes a finite-dimensional zero-diagonal Jacobi matrix employed as its initial condition. This differential equation is closely related to the one introduced by M. Kac and P. Van Moerbeke in 1975, although our approach to prove the key properties of this o.d.e. differs from the techniques developed by them. We show that our o.d.e. can be represented as a double bracket differential equation similar to the one studied by R.W. Brockett in 1991.

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