On phenomenon of scattering on resonances associated with discretisation of systems with fast rotating phase

TL;DR

This paper investigates how numerical integration of systems with fast rotating phases can introduce artificial phenomena, specifically scattering on resonances, that are not present in the original continuous-time systems.

Contribution

It reveals the emergence of resonance scattering phenomena in numerical solutions of systems with fast rotating phases, highlighting intrinsic differences from continuous systems.

Findings

Numerical solutions exhibit resonance scattering absent in original systems.

Discretization can induce artificial dynamical phenomena.

Fast rotating phases are sensitive to numerical discretization effects.

Abstract

Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of system with one fast rotating phase lead to a situation of such kind: numerical solution demonstrate phenomenon of scattering on resonances that is absent in the original system.