Eur. Phys. J. Special Topics 223, 2953–2958 (2014)
https://doi.org/10.1140/epjst/e2014-02308-6

Regular Article

Time-dependent properties in two-dimensional and Hamiltonian mappings

¹ Instituto de Física da USP, Cidade Universitária, 05314-970 São Paulo, SP, Brazil
² UNESP, Univ. Estadual Paulista, Câmpus São João da Boa Vista, São João da Boa Vista SP, Brazil
³ Departamento de Física e Matemática, Univ. Federal de São João del-Rei, UFSJ, Rod. MG 443, Km 7, Fazenda do Cadete, 36420-000 Ouro Branco, MG, Brazil
⁴ UNESP, Univ. Estadual Paulista, câmpus de Rio Claro, IGCE, Departamento de Física, Av. 24A, 1515, Bela Vista, CEP : 13506-900, Rio Claro, SP, Brazil

^a e-mail: livorati@rc.unesp.br

Received: 31 May 2014
Revised: 17 October 2014
Published online: 10 December 2014

Abstract

Some scaling properties for chaotic orbits in a family of two-dimensional Hamiltonian mappings are studied. The phase space of the model exhibits chaos and may have mixed structure with periodic islands, chaotic seas and invariant spanning curves. Average properties of the action variable in the chaotic sea are obtained as a function of time (t). From scaling arguments, critical exponents for the ensemble average of the action variable are obtained. Scaling invariance is obtained as a function of the control parameter that controls the intensity of the nonlinearity.