Artigo Revisado por pares

Systematic search for wide periodic windows and bounds for the set of regular parameters for the quadratic map

2017; American Institute of Physics; Volume: 27; Issue: 5 Linguagem: Inglês

10.1063/1.4983172

ISSN

1527-2443

Autores

Zbigniew Galias,

Tópico(s)

Quantum chaos and dynamical systems

Resumo

An efficient method to find positions of periodic windows for the quadratic map f(x)=ax(1-x) and a heuristic algorithm to locate the majority of wide periodic windows are proposed. Accurate rigorous bounds of positions of all periodic windows with periods below 37 and the majority of wide periodic windows with longer periods are found. Based on these results, we prove that the measure of the set of regular parameters in the interval [3,4] is above 0.613960137. The properties of periodic windows are studied numerically. The results of the analysis are used to estimate that the true value of the measure of the set of regular parameters is close to 0.6139603.

Referência(s)