arXiv:2108.07434 Abstract | arXiv Analytics

arXiv:2108.07434 [math.DS]Abstract References Reviews Resources

Poincaré-Hopf theorem for hybrid systems

Published 2021-08-17Version 1

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).

Comments: 6 pages, 1 figure, comments welcome. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Categories: math.DS, cs.RO, math.AT

Subjects: 37C25, 47H10, 34A38, 93C30

Keywords: hybrid systems, poincaré-hopf theorem, arbitrary multivalued maps, constant dimension, guard sets

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