It is well known that, generically, integrable Hamiltonian systems subjected to small, time-dependent perturbations, generate some orbits that experience significant energy growth. Moreover, the external perturbation can be effectively used as a control system, in order to drive orbits from one given location to another. In this work, we study the effect of random time-dependent perturbations on integrable Hamiltonian systems. The aim is to exploit the interplay between deterministic and stochastic behavior in order to obtain orbits whose energy follows any prescribed pathway in energy space. One, and not the least, motivation for this work is to extend results on the `Arnold diffusion problem' to the context of random dynamical systems, exploring the potential of random dynamical systems tools and formalism when applied to a problems usually studied in a Hamiltonian environment.

ENERGY DRIFT IN RANDOMLY PERTURBED HAMILTONIAN SYSTEMS

Anna Maria Cherubini;
2022

Abstract

It is well known that, generically, integrable Hamiltonian systems subjected to small, time-dependent perturbations, generate some orbits that experience significant energy growth. Moreover, the external perturbation can be effectively used as a control system, in order to drive orbits from one given location to another. In this work, we study the effect of random time-dependent perturbations on integrable Hamiltonian systems. The aim is to exploit the interplay between deterministic and stochastic behavior in order to obtain orbits whose energy follows any prescribed pathway in energy space. One, and not the least, motivation for this work is to extend results on the `Arnold diffusion problem' to the context of random dynamical systems, exploring the potential of random dynamical systems tools and formalism when applied to a problems usually studied in a Hamiltonian environment.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/472226
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