On variational systems along the trajectories of a stable compact invariant set of an autonomous complex-analytic system of differential equations
Let \(E \in \mathbb{C}^n\) be a stable compact invariant set of the autonomous complex-analytic system \(\dot{w}=f(w)\). The author shows that there exists a dense set \(E^* \subset E\) such that every variational equation along an orbit through a point \(w^* \in E\) is proper, i.e. the sum of the Lyapunov exponents equals the average NEWLINE\[NEWLINE\lim_{t\to\infty} 1/t \int_0^t \text{Re} [\text{Sp} \frac{\partial f}{\partial w}(w(t,w^*))]dt.NEWLINE\]NEWLINE The author also gives a condition for \(E^* = E\).
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