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Dense Analytic Curves Generated by Iterations of Complex Periodic Functions

Dense Analytic Curves Generated by Iterations of Complex Periodic Functions The present paper is devoted to finding the classes of complex periodic functions whose iterations map lines into dense subsets of the complex plane. We distinguish a class of functions such that its second iterations map almost all oblique lines into dense sets. A class of complex periodic functions are obtained whose third iterations of any oblique line generate dense subsets of the complex plane. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Dense Analytic Curves Generated by Iterations of Complex Periodic Functions

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Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-019-00262-3
Publisher site
See Article on Publisher Site

Abstract

The present paper is devoted to finding the classes of complex periodic functions whose iterations map lines into dense subsets of the complex plane. We distinguish a class of functions such that its second iterations map almost all oblique lines into dense sets. A class of complex periodic functions are obtained whose third iterations of any oblique line generate dense subsets of the complex plane.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 5, 2019

References