Graphs associated with the map in finite fields of characteristic three and five

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• 作者：S. Ugolini ^{sugolini@gmail.com}
• 关键词：Arithmetic dynamical systems ; Finite fields ; Elliptic curves
• 刊名：Journal of Number Theory
• 出版年：2013
• 出版时间：April, 2013
• 年：2013
• 卷：133
• 期：4
• 页码：1207-1228
• 全文大小：259 K

文摘

Text

In a previous paper the graphs associated with the iterations of the map ? which takes an element x of a finite field of characteristic two to were studied, exploiting the relation between ? and the duplication map over Koblitz curves. While in odd characteristic the graphs associated with ? seem not to present notable symmetries, these are present in characteristic three and five. In fact, while in characteristic three the map ? is conjugated to the inverse of the square mapping, in characteristic five it is related to an endomorphism of a certain elliptic curve. Relying on these considerations we describe the structure of the graphs in finite fields of characteristic three and five and present a computational procedure for constructing examples in any characteristic.

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