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Artículo

Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river

Cincotta, Pablo MiguelIcon ; Efthymiopoulos, C.; Giordano, Claudia MarcelaIcon ; Mestre, Martin FedericoIcon
Fecha de publicación: 01/2014
Editorial: Elsevier Science
Revista: Physica D - Nonlinear Phenomena
ISSN: 0167-2789
Idioma: Inglés
Tipo de recurso: Artículo publicado
Clasificación temática:
Astronomía

Resumen

We present theoretical and numerical results pointing towards a strong connection between the estimates for the diffusion rate along simple resonances in multidimensional nonlinear Hamiltonian systems that can be obtained using the heuristic theory of Chirikov and a more formal one due to Nekhoroshev. We show that, despite a wide-spread impression, the two theories are complementary rather than antagonist. Indeed, although Chirikov’s 1979 review has thousands of citations, almost all of them refer to topics such as the resonance overlap criterion, fast diffusion, the Standard or Whisker Map, and not to the constructive theory providing a formula to measure diffusion along a single resonance. However, as will be demonstrated explicitly below, Chirikov’s formula provides values of the diffusion coefficient which are quite well comparable to the numerically computed ones, provided that it is implemented on the so-called optimal normal form derived as in the analytic part of Nekhoroshev’s theorem. On the other hand, Chirikov’s formula yields unrealistic values of the diffusion coefficient, in particular for very small values of the perturbation, when used in the original Hamiltonian instead of the optimal normal form. In the present paper, we take advantage of this complementarity in order to obtain accurate theoretical predictions for the local value of the diffusion coefficient along a resonance in a specific 3DoF nearly integrable Hamiltonian system. Besides, we compute numerically the diffusion coefficient and a full comparison of all estimates is made for ten values of the perturbation parameter, showing a very satisfactory agreement.
Palabras clave: Chaos , Instability , Dynamics , Arnold Diffusion
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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Atribución-NoComercial-SinDerivadas 2.5 Argentina (CC BY-NC-ND 2.5 AR)
Identificadores
URI: http://hdl.handle.net/11336/15512
URL: http://www.sciencedirect.com/science/article/pii/S0167278913002819
DOI: http://dx.doi.org/10.1016/j.physd.2013.10.005
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Articulos(IALP)
Articulos de INST.DE ASTROFISICA LA PLATA
Citación
Cincotta, Pablo Miguel; Efthymiopoulos, C.; Giordano, Claudia Marcela; Mestre, Martin Federico; Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river; Elsevier Science; Physica D - Nonlinear Phenomena; 266; 1-2014; 49-64
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