Calculation of the Statistical Properties in Intermittency Using the Natural Invariant Density

Symmetry

卷:13

Sergio Elaskar¹  Ezequiel del Río²  Denis Lorenzón³ 

[1] Departamento de Aeronáutica, Instituto de Estudios Avanzados en Ingeniería y Tecnología (IDIT), FCEFyN, Universidad Nacional de Córdoba and CONICET, Córdoba 5000, Argentina;

[2] Departamento de Física Aplicada, ETSIAE, Universidad Politécnica de Madrid, 28040 Madrid, Spain;

[3] Instituto de Estudios Avanzados en Ingeniería y Tecnología (IDIT), Universidad Nacional de Córdoba and CONICET, Córdoba 5000, Argentina;

关键词: chaotic intermittency;    maps;    reinjection probability density function;    invariant density;   

DOI  :  10.3390/sym13060935

来源: DOAJ

【 摘 要 】

We use the natural invariant density of the map and the Perron–Frobenius operator to analytically evaluate the statistical properties for chaotic intermittency. This study can be understood as an improvement of the previous ones because it does not introduce assumptions about the reinjection probability density function in the laminar interval or the map density at pre-reinjection points. To validate the new theoretical equations, we study a symmetric map and a non-symmetric one. The cusp map has symmetry about $x=0$, but the Manneville map has no symmetry. We carry out several comparisons between the theoretical equations here presented, the M function methodology, the classical theory of intermittency, and numerical data. The new theoretical equations show more accuracy than those calculated with other techniques.

【 授权许可】

Unknown