Bifurcation of Control Sets at Singular Points

Stefan M. Grünvogel (1999)
Equadiff 99, pp. 853-855 (2000)

Abstract

We look at a control affine system in ℝ^d with a singular point x* ∈ ℝ^d. Motivated by the example of the perturbed Duffing-van der Pol equation we show, that under a condition on the Lyapunov exponents, there exists a control set D ⊂ ℝ^d with nonvoid interior such that x* ∈ closure(D).