Localized control for non-resonant Hamiltonian systems

DOI10.1088/0951-7715/18/1/021zbMATH Open1109.37047arXivnlin/0405056OpenAlexW2004189420MaRDI QIDQ4655113

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Publication date: 10 March 2005

Published in: Nonlinearity (Search for Journal in Brave)

Abstract: We present a method of localised control of chaos in Hamiltonian systems. The aim is to modify the perturbation locally by a small control term which makes the controlled Hamiltonian more regular. We provide an explicit expression for the control term which is able to recreate invariant (KAM) tori without modifying other parts of phase space. We apply this method of localised control to a forced pendulum model, to the delta-kicked rotor (standard map) and to a non-twist Hamiltonian.

Full work available at URL: https://arxiv.org/abs/nlin/0405056

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Nonlinear systems in control theory (93C10) Hamilton's equations (70H05) Control of mechanical systems (70Q05) Dynamical systems in control (37N35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (3)

High-order control for symplectic maps ⋮ Reducing or enhancing chaos using periodic orbits ⋮ Hamiltonian control of magnetic field lines: computer assisted results proving the existence of KAM barriers

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