Multifractal spectrum of quotients of Birkhoff averages for a family of quadratic maps. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Mesón, Alejandro; Vericat, Fernando
• Is Part Of: Journal of dynamical systems and geometric theories. Volume 16:Issue 1(2018)
• Page Start: 17
• Page End: 32
• Publication Date: 2018-01-02
• Subjects: 37C45 -- 37B40; Multifractal spectrum -- Quotients of Birkhoff averages -- Benedicks-Carleson maps; Differentiable dynamical systems -- Periodicals; Geometry -- Periodicals; Differentiable dynamical systems; Geometry; Periodicals; 515.39
• DOI: 10.1080/1726037X.2017.1413064
• Languages: English
• ISSNs: 1726-037X

Abstract

ABSTRACT: In a recent article, Chung and Takahashi (Erg. Th & Dynan. Sys. 34, 1116 (2014)) effected a multifractal description of the Birkhoff spectrum for a set of quadratic one dimensional functions known as the Benedicks-Carleson maps . They obtained a variational formula for the dimension spectrum of Birkhoff averages. In this article we try to complete the analysis studying the spectrum of quotients of Birkhoff averages.