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Observability of control systems for polynomial inputs and genericity

Philippe Jouan (2001)

Applicationes Mathematicae

We consider smooth single-input, two-output systems on a compact manifold X. We show that the set of systems that are observable for any polynomial input whose degree is less than or equal to a given bound contains an open and dense subset of the set of smooth systems.

On boundary slopes of immersed incompressible surfaces

Mark D. Baker (1996)

Annales de l'institut Fourier

Let M be a compact, orientable, irreducible 3-manifold with M a torus. We show that there can be infinitely many slopes on M realized by the boundary curves of immersed, incompressible, - incompressible surfaces in M which are embedded in a neighborhood of M .

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