S-integral preperiodic points for monomial semigroups over number fields

2024/02/21 by Young, Marley
#11G50 #11J86 #37P05 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.13713

Abstract

We consider semigroup dynamical systems defined by several monnomials over a number field K. We prove a finiteness result for preperiodic points of such systems which are S-integral with respect to a non-preperiodic point β, which is uniform as β varies over number fields of bounded degree. This generalises results of Baker, Ih and Rumely, which were made uniform by Yap, and verifies a special case of a natural generalisation of a conjecture of Ih.

Related

• On algebraic integers of bounded house and preperiodicity in polynomial\n semigroup dynamics
• Uniform bounds on S-integral preperiodic points for chebyshev polynomials
• Monomial Dynamical Systems of Dimension One over Finite Fields
• A finiteness property for preperiodic points of Chebyshev polynomials
• Effective bounds on S-integral preperiodic points for polynomials