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

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 Nekhoroshe...

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Detalles Bibliográficos
Autores principales: Cincotta, Pablo Miguel, Efthymiopoulos, C., Giordano, Claudia Marcela, Mestre, Martín Federico
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2014
Materias:
Astronomía
Física
Ciencias Naturales
Ciencias Exactas
Chaos
Instability
Dynamics
Arnold diffusion
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/93845
http://www.sciencedirect.com/science/article/pii/S0167278913002819
https://arxiv.org/abs/1310.3158
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-93845
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Astronomía
Física
Ciencias Naturales
Ciencias Exactas
Chaos
Instability
Dynamics
Arnold diffusion
spellingShingle Astronomía
Física
Ciencias Naturales
Ciencias Exactas
Chaos
Instability
Dynamics
Arnold diffusion
Cincotta, Pablo Miguel
Efthymiopoulos, C.
Giordano, Claudia Marcela
Mestre, Martín Federico
Chirikov and Nekhoroshev diffusion estimates : Bridging the two sides of the river
topic_facet Astronomía
Física
Ciencias Naturales
Ciencias Exactas
Chaos
Instability
Dynamics
Arnold diffusion
description 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.
format Articulo
Preprint
author Cincotta, Pablo Miguel
Efthymiopoulos, C.
Giordano, Claudia Marcela
Mestre, Martín Federico
author_facet Cincotta, Pablo Miguel
Efthymiopoulos, C.
Giordano, Claudia Marcela
Mestre, Martín Federico
author_sort Cincotta, Pablo Miguel
title Chirikov and Nekhoroshev diffusion estimates : Bridging the two sides of the river
title_short Chirikov and Nekhoroshev diffusion estimates : Bridging the two sides of the river
title_full Chirikov and Nekhoroshev diffusion estimates : Bridging the two sides of the river
title_fullStr Chirikov and Nekhoroshev diffusion estimates : Bridging the two sides of the river
title_full_unstemmed Chirikov and Nekhoroshev diffusion estimates : Bridging the two sides of the river
title_sort chirikov and nekhoroshev diffusion estimates : bridging the two sides of the river
publishDate 2014
url http://sedici.unlp.edu.ar/handle/10915/93845
http://www.sciencedirect.com/science/article/pii/S0167278913002819
https://arxiv.org/abs/1310.3158
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