Functional graphs of rational maps induced by endomorphisms of ordinary elliptic curves over finite fields

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Abstract

In this paper we study the dynamics of rational maps induced by endomorphisms of ordinary elliptic curves defined over finite fields. For any such map we describe the cycle and the tree structures of the associated graphs.

Keywords

Dynamical systems Finite fields Arithmetic dynamics Endomorphisms of elliptic curves 

Mathematics Subject Classification

37P55 37P05 11G20 

Notes

Acknowledgements

The author is grateful to the anonymous Reviewer for the careful reading of the manuscript and the valuable comments and suggestions.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Università degli Studi di TrentoTrentoItaly

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