Artículos de revistas
The role of extreme orbits in the global organization of periodic regions in parameter space for one dimensional maps
Fecha
2016-04-22Registro en:
Physics Letters, Section A: General, Atomic and Solid State Physics, v. 380, n. 18-19, p. 1610-1614, 2016.
0375-9601
10.1016/j.physleta.2016.02.049
2-s2.0-84961128161
2-s2.0-84961128161.pdf
Autor
Universidade Estadual Paulista (Unesp)
Univ. São Paulo
Universidade Federal de São Paulo (UNIFESP)
Imperial College London
Abdus Salam International Center for Theoretical Physics
Institución
Resumen
We show that extreme orbits, trajectories that connect local maximum and minimum values of one dimensional maps, play a major role in the parameter space of dissipative systems dictating the organization for the windows of periodicity, hence producing sets of shrimp-like structures. Here we solve three fundamental problems regarding the distribution of these sets and give: (i) their precise localization in the parameter space, even for sets of very high periods; (ii) their local and global distributions along cascades; and (iii) the association of these cascades to complicate sets of periodicity. The extreme orbits are proved to be a powerful indicator to investigate the organization of windows of periodicity in parameter planes. As applications of the theory, we obtain some results for the circle map and perturbed logistic map. The formalism presented here can be extended to many other different nonlinear and dissipative systems.