Definition
If
is a linear non-autonomous dynamical system in Rn with fundamental solution matrix Φ(t), Φ(0) = I, then the equilibrium point 0 is said to have an exponential dichotomy if there exists a (constant) matrix P such that P2 = P and positive constants K, L, α, and β such that
and
If furthermore, L = 1/K and β = α, then 0 is said to have a uniform exponential dichotomy.
The constants α and β allow us to define the spectral window of the equilibrium point, (−α, β).
Read more about this topic: Exponential Dichotomy
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