2019/07/02 by Ruan, Haibo, Zanelli, Jorge
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1907.01473
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 refines and extends the usual topological index in accordance with the Poincaré-Hopf Theorem.