On continuum dynamics
The theory of continuous dynamical systems is developed with an intrinsic geometric approach based on the action principle formulated in the velocity-time manifold. By endowing the finite dimensional ...
The theory of continuous dynamical systems is developed with an intrinsic geometric approach based on the action principle formulated in the velocity-time manifold. By endowing the finite dimensional ...
Basic results on the equations of magnetohydrodynamics of partially ionized inviscid plasmas
The equations of evolution of partially ionized plasmas have been far more studied in one of their many simplifications than in its original form. They present a relation between the velocity of each ...
The equations of evolution of partially ionized plasmas have been far more studied in one of their many simplifications than in its original form. They present a relation between the velocity of each ...
Dual Lindstedt series and Kolmogorov–Arnol'd–Moser theorem
J. Math. Phys. 50, 102904 (2009); doi:10.1063/1.3250190
Published 28 October 2009
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We prove that there exists a Lindstedt series that holds when a Hamiltonian is driven by a perturbation going to infinity. This series appears to be dual to a standard Lindstedt series as it can be obtained by interchanging the role of the perturbation and the unperturbed system. The existence of this dual series implies that a dual Kolmogorov–Arnol'd–Moser (KAM) theorem holds, and when a leading order Hamiltonian exists, which is nondegenerate, the effect of tori reforming can be observed with a system passing from regular motion to fully developed chaos and back to regular motion with the reappearance of invariant tori. We apply these results to a perturbed harmonic oscillator, proving numerically the appearance of tori reforming. Tori reforming appears as an effect that limits chaotic behavior to a finite range of parameter space of some Hamiltonian systems. Dual KAM theorem, as proved here, applies when the perturbation, combined with a kinetic term, provides again an integrable system.
©2009 American Institute of Physics
| History: | Received 2 June 2009; accepted 8 September 2009; published 28 October 2009 |
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http://link.aip.org/link/?JMAPAQ/50/102904/1 |
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