Neutral state of dynamical system?

10 October 2022 1 5K Report

Hello all,

Is it possible to have multiple (more than 3) neutral-state (center) in a dynamical system? If yes, please provide some references.

Thank you.

Evgeny Malkovich

Yes, it is possible. The corresponding vector filed is constructed in the proof of Poincare-Hopf Theorem. Every vertex of triangulation is a center (i.e. a zero of vector field with index 1).

http://www-personal.umich.edu/~alexmw/PoincareHopf.pdf

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