Open Access
2010 Joining Polynomial and Exponential Combinatorics for Some Entire Maps
Antonio Garijo, Xavier Jarque, Mónica Moreno Rocha
Publ. Mat. 54(1): 113-136 (2010).


We consider families of entire transcendental maps given by $F_{\lambda,m} (z) = \lambda z^m \exp(z) $ where $m \ge 2$. All these maps have a superattracting fixed point at $z=0$ and a free critical point at $z=-m$. In parameter planes we focus on the capture zones, i.e., we consider $\lambda$ values for which the free critical point belongs to the basin of attraction of $z=0$. We explain the connection between the dynamics near zero and the dynamics near infinity at the boundary of the immediate basin of attraction of the origin, thus, joining together exponential and polynomial behaviors in the same dynamical plane.


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Antonio Garijo. Xavier Jarque. Mónica Moreno Rocha. "Joining Polynomial and Exponential Combinatorics for Some Entire Maps." Publ. Mat. 54 (1) 113 - 136, 2010.


Published: 2010
First available in Project Euclid: 8 January 2010

zbMATH: 1180.37064
MathSciNet: MR2603591

Primary: 30D20 , 37F20

Keywords: Combinatorial dynamics , Julia sets , polynomial-like maps

Rights: Copyright © 2010 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.54 • No. 1 • 2010
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