Reducing or enhancing chaos using periodic orbits

Abstract

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.

References in corpus (3)

• Channelling chaos by building barriers
• Control of stochasticity in magnetic field lines
• Localised control for non-resonant Hamiltonian systems

Cited by in corpus (5)

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• Stabilizing the intensity of a wave amplified by a beam of particles
• How periodic orbit bifurcations drive multiphoton ionization
• Periodic orbit bifurcations as an ionization mechanism: The bichromatically driven hydrogen atom