Hamiltonian form for general autonomous ODE systems: Low dimensional examples
arXiv:2008.12176
Abstract
Paper is devoted to maintaining the simple objective: We want to provide Hamiltonian canonical form for autonomous dynamical system reducible to even-dimensional one. Along the road we construct new class of conserved quantities, called effectively conserved, that have dissimilar properties to traditional first integrals (e.g. differential of effectively conserved quantity being a Pfaffian form). We do not confine the discussion to physics; we consider examples from biology and chemistry, giving direct recipe for how to engage the framework in occurring problems. Perspective for future application in geometric numerical methods is given.
arXiv comment18 pages