Kupka, Ivan A. K. The ubiquity of Fuller’s phenomenon. (English) Zbl 0739.49001 Nonlinear controllability and optimal control, Lect. Workshop, New Brunswick/NJ (USA) 1987, Pure Appl. Math., Marcel Dekker 133, 313-350 (1990). [For the entire collection see Zbl 0699.00040.]The following phenomenon which was discovered by Fuller in the case of a certain two-dimensional optimal control problem is well known: the unique optimal trajectory joining an arbitrary point and the origin switches an infinite number of times alternatively on two branches of two different parabolas. In the present study, the author gives sufficient conditions for the above property (mainly the fact that the switching set is not finite) to occur in a general system and shows that it is generic. Reviewer: C.Popa (Iaşi) Cited in 26 Documents MSC: 49J15 Existence theories for optimal control problems involving ordinary differential equations 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems Keywords:switching conditions; infinite switching set; optimal trajectory Citations:Zbl 0699.00040 PDFBibTeX XMLCite \textit{I. A. K. Kupka}, in: Invariance of extremals. . 313--350 (1990; Zbl 0739.49001)