2021/04/30 by Gorni, Gianluca, Scomparin, Mattia, Zampieri, Gaetano
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2104.14793
We describe a recipe to generate "nonlocal" constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechanical systems, from which we can deduce global existence and estimates of solutions under fairly general assumptions. Then we review a generalization to Euler-Lagrange ODEs of order higher than two, leading to first integrals for the Pais-Uhlenbeck oscillator and other systems. Future developments may include adaptations of the theory to Euler-Lagrange PDEs.