Dynamics of the meromorphic families $f_\lambda=\lambda \tan^pz^q$

نویسندگان

چکیده

This paper continues our investigation of the dynamics families transcendental meromorphic functions with finitely many singular values all which are finite. Here we look at a generalization family polynomials $P_a(z)=z^{d-1}(z- \frac{da}{(d-1)})$, $f_{\lambda}=\lambda \tan^p z^q$. These have super-attractive fixed point, and, depending on $p$, one or two asymptotic values. Although dynamical properties generalize, existence an essential singularity and poles multiplicity greater than implies that significantly different techniques required here. Adding methods to standard ones, give description properties; in particular prove Julia set hyperbolic map is either connected locally Cantor set. We also parameter plane $f_{\lambda}$. Again there similarities differences from $P_a$ again new techniques. In particular, dense points boundaries components accessible along curves characterize these points.

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ژورنال

عنوان ژورنال: New Zealand journal of mathematics

سال: 2021

ISSN: ['1171-6096', '1179-4984']

DOI: https://doi.org/10.53733/135