Edson D Leonel et al 2011 J. Phys. A: Math. Theor. 44 302001 doi:10.1088/1751-8113/44/30/302001
Critical exponents for a transition from integrability to non-integrability via localization of invariant tori in the Hamiltonian system
FREE ARTICLEEdson D Leonel1, Juliano A de Oliveira1 and Farhan Saif1,2
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Critical exponents that describe a transition from integrability to non-integrability in a two-dimensional, nonlinear and area-preserving map are obtained via localization of the first invariant spanning curve (invariant tori) in the phase space. In a general class of systems, the position of the first invariant tori is estimated by reducing the mapping of the system to the standard mapping where a transition takes place from local to global chaos. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori whose position of the first of them depends on the control parameters. The formalism leads us to obtain analytically critical exponents that describe the behaviour of the average variable (action) along the chaotic sea. The result is compared to several models in the literature confirming the approach is of large interest. The formalism used is general and the procedure can be extended to many other different systems.
- PACS
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05.45.Pq Numerical simulations of chaotic systems
02.60.Cb Numerical simulation; solution of equations
- MSC
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34C28 Complex behavior, chaotic systems (See mainly 37Dxx)
37J30 Obstructions to integrability (nonintegrability criteria)
- Subjects
- Dates
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Issue 30 (29 July 2011)
Received 26 April 2011, in final form 15 June 2011
Published 4 July 2011
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Critical exponents for a transition from integrability to non-integrability via localization of invariant tori in the Hamiltonian system
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