The dynamics of \(\lambda+z+\exp(z)\)
type: Item
instance of: scholarly article
title: The dynamics of \(\lambda+z+\exp(z)\)
zbMATH Open document ID: 0941.37003
author: Peter Petek
author: Marjeta Škapin Rugelj
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-08-13T00:00:00Z
review text: The paper is devoted to a dynamics of the map \(f_\lambda(z)=\lambda+z+e^z\) both for \(\lambda>0\) and \(\lambda=\alpha+i\beta\), \(\beta\neq 0\). First of all, the authors prove that the set of points that share the same refined itinerary and tend monotonically to infinity lie on a Lipschitz curve (the case of \(\lambda>0\)). In the case of \(\lambda=\alpha+i\beta\), \(\beta\neq 0\), they prove that for some values of the parameter there exist invariant curves which divide the complex plane into bent stripes giving rise to symbolic dynamics similar to those in the first case.
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 37F20
zbMATH DE Number: 1216999
zbMATH Keywords: invariant curves
zbMATH Keywords: symbolic dynamics
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5724
OpenAlex ID: W2030552886
cites work: Q5593934
cites work: Wandering Domains in the Iteration of Entire Functions
cites work: Dynamics of exp (z)
cites work: Dynamics of entire functions near the essential singularity
cites work: Q3715382
cites work: LIMITING DYNAMICS FOR THE COMPLEX STANDARD FAMILY
cites work: A finiteness theorem for a dynamical class of entire functions
cites work: Julia set of the function \(z\exp(z+\mu)\)
cites work: Q3831746
cites work: Q3985929
DOI: 10.1006/JMAA.1997.5724
description: scientific article; zbMATH DE number 1216999