• Corpus ID: 195776437

Degeneracy Index and Poincar\'e-Hopf Theorem

  title={Degeneracy Index and Poincar\'e-Hopf Theorem},
  author={Haibo Ruan and Jorge Zanelli},
  journal={arXiv: Mathematical Physics},
  • H. RuanJ. Zanelli
  • Published 2 July 2019
  • Mathematics, Physics
  • arXiv: Mathematical Physics
A degenerate dynamical system is characterized by a state-dependent multiplier of the time derivative of the state in the time evolution equation. It can give rise to Hamiltonian systems whose symplectic structure possesses a non-constant rank throughout the phase space. Around points where the multiplier becomes singular, flow can experience abrupt and irreversible changes. We introduce a topological index for degenerate dynamical systems around these {\it degeneracy points} and show that it… 

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