MORSE INDEX FOR AUTONOMOUS LINEAR HAMILTONIAN SYSTEMS
Abstract
In this paper, we will derive a new formula for the Morse index for the linear Hamiltonian systems:$$ J \dot x+Ax=0, $$where matrix $J$ is the standard symplectic structure matrix of order $2N$ and $A$ is a constant, symmetric positive definite matrix of order $2N$, $N$ is any natural number.
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