English

Poincar\'{e}-Hopf theorem for hybrid systems

Dynamical Systems 2024-10-28 v1 Robotics Algebraic Topology

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).

Keywords

Cite

@article{arxiv.2108.07434,
  title  = {Poincar\'{e}-Hopf theorem for hybrid systems},
  author = {Matthew D. Kvalheim},
  journal= {arXiv preprint arXiv:2108.07434},
  year   = {2024}
}

Comments

6 pages, 1 figure, comments welcome. This work has been submitted to the IEEE for possible publication

R2 v1 2026-06-24T05:10:31.488Z