On period doubling phenomena and Sharkovskii type ordering for the family λ tan(z)
نویسندگان
چکیده
In this paper we prove that all the hyperbolic components of the family λ tan z except the punctured unit disk are simply connected. Then, restricting λ to the imaginary axis, We show that there is a “Sharkovskii-like” ordering of the periods of the hyperbolic components. Finally, again for λ in the imaginary axis, we show that period doubling phenomena occur.
منابع مشابه
Complex and Real Dynamics for the family λ tan(z)
This article is based on my lecture at the Complex Dynamics Workshop of the Research Institute of Mathematics at Kyoto University in October 2001. It is an exposition of joint work with Janina Kotus. The tangent family fλ(z) = λ tan(z) is the meromorphic analogue of the quadratic family z +c. The functions fλ(z) are characterized by their mapping properties: they are, up to scale, the only mero...
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