On the iterations of certain maps $x\mapsto k\cdot (x+x^{-1})$ over finite fields of odd characteristic

Abstract

In this paper we describe the dynamics of certain rational maps of the form $k\cdot (x+x^{-1})$ over finite fields of odd characteristic.

27 pages, expanded version with improved proofs and examples

References in corpus (3)

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

Cited by in corpus (4)

• 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
• Sequences of irreducible polynomials over odd prime fields via elliptic curve endomorphisms
• Dynamics of the $a$-map over residually finite Dedekind Domains and applications