Geodesic
Cyclic approximation to stasis
Electronic journal of differential equations, Tome 2009 (2009)
Neighborhoods of points in $\mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $\mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.
Classification : 37C10, 37C27
Keywords: two-cycles, stasis points, switching systems, piecewise smooth, relaxed controls 
@article{EJDE_2009__2009__a157,
     author = {Johnson,  Stewart D. and Rodu,  Jordan},
     title = {Cyclic approximation to stasis},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1186.37028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a157/}
}
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Johnson,  Stewart D.; Rodu,  Jordan. Cyclic approximation to stasis. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a157/