Application of the Slater criteria to localize invariant tori in Hamiltonian mappings

• Autor(a) principal: Huggler, Yoná H. [UNESP]
• Data de Publicação: 2022
• Outros Autores: Hermes, Joelson D. V. [UNESP], Leonel, Edson D. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• DOI: 10.1063/5.0103427
• Texto Completo: http://dx.doi.org/10.1063/5.0103427; http://hdl.handle.net/11449/245997

We investigate the localization of invariant spanning curves for a family of two-dimensional area-preserving mappings described by the dynamical variables I and θ by using Slater's criterion. The Slater theorem says there are three different return times for an irrational translation over a circle in a given interval. The returning time, which measures the number of iterations a map needs to return to a given periodic or quasi periodic region, has three responses along an invariant spanning curve. They are related to a continued fraction expansion used in the translation and obey the Fibonacci sequence. The rotation numbers for such curves are related to a noble number, leading to a devil's staircase structure. The behavior of the rotation number as a function of invariant spanning curves located by Slater's criterion resulted in an expression of a power law in which the absolute value of the exponent is equal to the control parameter γ that controls the speed of the divergence of θ in the limit the action I is sufficiently small.