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Volume of the hyperbolic cantor sets.
- Source :
- Dynamical Systems: An International Journal; Jun2020, Vol. 35 Issue 2, p185-196, 12p
- Publication Year :
- 2020
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- CANTOR sets
LEBESGUE measure
Subjects
Details
- Language :
- English
- ISSN :
- 14689367
- Volume :
- 35
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Dynamical Systems: An International Journal
- Publication Type :
- Academic Journal
- Accession number :
- 144525739
- Full Text :
- https://doi.org/10.1080/14689367.2019.1659754