| Abstract: |
| An important concept in the study of nonautonomous linear differential systems is that
of exponential separation. It is closely related to the concept of exponential dichotomy. Also it has played a key
role in the theory of Lyapunov exponents. Usually in the study of exponential
separation, it is assumed that the coefficient matrix is bounded in norm. Our first aim
here is to develop a theory of exponential separation which applies to unbounded
systems. It turns that in order to have a reasonable theory, it is necessary to add the
assumption that the angle between the two separated subspaces is bounded below.
This is what is meant by strong exponential separation. Our second aim is to show that
if a bounded linear Hamiltonian system is exponentially separated into two subspaces
of the same dimension, then it must have an exponential dichotomy. |
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