# American Institute of Mathematical Sciences

May  2013, 33(5): 1883-1890. doi: 10.3934/dcds.2013.33.1883

## No invariant line fields on escaping sets of the family $\lambda e^{iz}+\gamma e^{-iz}$

 1 Department of Mathematics, Graduate Center, CUNY, 365 Fifth Avenue, New York, NY 10016, United States 2 Department of Mathematics, Queens College, Flushing, NY 11367, United States 3 Department of Mathematics, Nanjing University, Nanjing 210090, China

Received  September 2011 Revised  August 2012 Published  December 2012

Consider the family $f_{\lambda, \gamma}(z) = \lambda e^{iz}+\gamma e^{-iz}$ where $\lambda$ and $\gamma$ are non-zero complex numbers. It contains the sine family $\lambda \sin z$ and is a natural extension of the sine family. We give a direct proof of that the escaping set $I_{\lambda, \gamma}$ of $f_{\lambda, \gamma}$ supports no $f_{\lambda,\gamma}$-invariant line fields.
Citation: Tao Chen, Yunping Jiang, Gaofei Zhang. No invariant line fields on escaping sets of the family $\lambda e^{iz}+\gamma e^{-iz}$. Discrete & Continuous Dynamical Systems, 2013, 33 (5) : 1883-1890. doi: 10.3934/dcds.2013.33.1883
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