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Poincaré-Hopf theorem for hybrid systems (2108.07434v1)
Published 17 Aug 2021 in math.DS, cs.RO, and math.AT
Abstract: A generalization of the Poincar\'{e}-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).