Volume of the hyperbolic cantor sets. Issue 2 (2nd April 2020)

• Record Type: Journal Article
• Authors: Akhadkulov, Habibulla; Jiang, Yunping
• Is Part Of: Dynamical systems. Volume 35:Issue 2(2020)
• Page Start: 185
• Page End: 196
• Publication Date: 2020-04-02
• Subjects: Hyperbolic cantor sets -- Lebesgue measure -- expending map; 37E05 -- 26A16 -- 26A18; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1659754
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: In this paper, we study hyperbolic Cantor sets on the line. We prove that the Lebesgue measure of a hyperbolic Cantor set generated by a degree two expanding map satisfying a certain Zygmund condition is zero. Moreover, we show that for any ρ ∈ ( 0, 1 ) there exists a C 1 -smooth degree two expanding map f such that the Lebesgue measure of the hyperbolic Cantor set generated by f is ρ .