An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action

The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, θ and controlled by two con...

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Detalhes bibliográficos
Autores: Leonel, Edson D. [UNESP], Kuwana, Célia M. [UNESP]
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:Brasil
Recursos:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/170381
Acesso em linha:http://dx.doi.org/10.1007/s10955-017-1920-x
http://hdl.handle.net/11449/170381
Access Level:acceso abierto
Palavra-chave:Critical exponents
Diffusion equation
Phase transition
Scaling laws
Descrição
Resumo:The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, θ and controlled by two control parameters: (i) ϵ, controlling the nonlinearity of the system, particularly a transition from integrable for ϵ= 0 to non-integrable for ϵ≠ 0 and; (ii) γ denoting the power of the action in the equation defining the angle. For ϵ≠ 0 the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.