Journal of the Korean Mathematical Society (대한수학회지)
- Volume 33 Issue 1
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- Pages.47-55
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
ASYMPTOTIC BEHAVIOR OF LEBESGUE MEASURES OF CANTOR SETS ARISING IN THE DYNAMICS OF TANGENT FAMILY $$T_ALPHA (THETA) ALPHA TAN(THETA/2)$
- Kim, Hong-Oh (Department of Mathematics KAIST ) ;
- Kim, Jun-Kyo (Department of Mathematics KAIST ) ;
- Kim, Jong-Wan (Department of Mathematics KAIST )
- Published : 1996.02.01
Abstract
Let $0 < \alpha < 2$ and let $T_\alpha (\theta) = \alpha tan(\theta/2)$. $T_\alpha$ has an attractive fixed point at $\theta = 0$. We denote by $C(\alpha)$ the set of points in $I = [-\pi, \pi]$ which are not attracted to $\theta = 0$ by the succesive iterations of $T_\alpha$. That is, $C(\alpha)$ is the set of points in I where the dynamics of $T_\alpha$ is chaotic.