4 papers
Algebraic Detection of Tube Rupture via a Cubic Discriminant Criterion
Johannes Hagel
We investigate the rupture of invariant tubes in a class of nonautonomous dynamical systems arising from time-dependent Ermakov-type equations. Starting from an exactly tube-integr…
Tube Rupture in Aperiodic Nonlinear Oscillators: Theory and Simulation
Johannes Hagel
We study the long-term behaviour of the nonlinear, aperiodically and parametrically forced oscillator z'' + z + g(tau) z^2 = 0, g(tau) = y(tau)^(-5/2), where y(tau) is the strictly…
Tube Integrability in a Time-Dependent Nonlinear Oscillator
Johannes Hagel
We study the nonlinear oscillator z'' + omega^2 z + g(t) z^2 = 0 with a time-dependent coefficient g(t). We show that this equation admits an exact quadratic invariant I(z,p,t) pro…
Integrable nonlinear oscillators with polynomial invariants: construction, Poincare geometry, and an analytic stability boundary
Johannes Hagel
Starting from the nonlinear ODE with , we show that after a suitable normal-form reduction of any Hill equation one may, without loss of gener…