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 there exists a -smooth degree two expanding map f such that the Lebesgue measure of the hyperbolic Cantor set generated by f is ρ.
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