Graphs associated with the map $x\mapsto x+x^{-1}$ in finite fields of characteristic five

Abstract

In this paper we study the structure of the graphs associated with the iterations of the map $x\mapsto x+x^{-1}$ over finite fields of characteristic five.

17 pages, 1 example. Some proofs have been expanded. Fixed typos. arXiv admin note: text overlap with arXiv:1107.4565

References in corpus (1)

• Graphs associated with the map $x\mapsto x+x^{-1}$ in finite fields of characteristic two

Cited by in corpus (4)

• On the iterations of certain maps $x\mapsto k\cdot (x+x^{-1})$ over finite fields of odd characteristic
• Functional graphs of rational maps induced by endomorphisms of ordinary elliptic curves over finite fields
• Sequences of irreducible polynomials without prescribed coefficients over odd prime fields
• Dynamics of the $a$-map over residually finite Dedekind Domains and applications