Centre (dynamics)

Nonlinear centres with conserved quantities

Consider the differential system with differentiable . Suppose there exists a conserved quantity and that is an isolated fixed point. If is a local extremum of , then there exists a neighbourhood of containing only orbits.1 #m/thm/dynamics/flow

Proof

#missing/proof


#state/tidy | #lang/en | #SemBr

Footnotes

  1. 2024. Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering, §6.5, p. 180