Abstract
We investigate the effects of round-off errors on quasi-periodic motions in a linear symplectic planar map. By discretizing coordinates uniformly we transform this map into a permutation of Z2, and study motions near infinity, which correspond to a fine discretization. We provide numerical evidence that all orbits are periodic and that the averageorder of the period grows linearly with the amplitude. The discretization induces fluctuations of the invariant of the continuum system. We investigate the associated transport processfor time scales shorter than the period, and we provide numerical evidence that the limiting behaviour is a random walk where the step size is modulated by a quasi-periodic function. For this stochastic process we compute the transport coefficients explicitly, by constructing their generating function. These results afford a probabilistic description of motions on a classical invariant torus.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
