Poincaré-Hopf theorem for hybrid systems

08/17/2021

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by   Matthew D. Kvalheim, et al.

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A generalization of the Poincaré-Hopf index theorem applicable to hybrid dynamical systems is obtained. For the hybrid systems considered, guard sets are not assumed to be smooth; distinct "modes" are not assumed to have constant dimension; and resets are arbitrary multivalued maps (relations).