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BIRS Workshop Lecture Videos

Limit cycles of planar vector fields, Hilbertâ s 16th problem and o-minimality Speissegger, Patrick


Recent work links certain aspects of the second part of Hilbertâ s 16th problem (H16) to the theory of o-minimality. One of these aspects is the generation and destruction of limit cycles in families of planar vector fields, commonly referred to as â bifurcationsâ . I will outline the significance of bifurcations for H16 and explain how logicâ in particular, o-minimalityâ can be used to understand them well enough to be able to count limit cycles.

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