A new family of expansions of real numbers

2024/06/16 by Neunhäuserer, Jörg
#11K55 #26A30 #28A80 #37A44 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2406.10919

Abstract

For α>1 we represent a real number in (0,1] in the form ∑_i=1^∞(α-1)^i-1α^-(d₁+…+d_i) with d_i∈ℕ. We discuss ergodic theoretical and dimension theoretical aspects of this expansion. Furthermore we study their base-change-transformation.

Related

• Unique expansions of real numbers
• Somme des chiffres et changement de base
• Topology of univoque sets in real base expansions
• Universal β-expansions
• Optimal expansions in non-integer bases