Affine actions of a free semigroup on the real line

Abstract

We consider actions of the free semigroup with two generators on the real line, where the generators act as affine maps, one contracting and one expanding, with distinct fixed points. Then every orbit is dense in a half-line, which leads to the question whether it is, in some sense, uniformly distributed. We present answers to this question for various interpretations of the phrase ``uniformly distributed''.

Cited by in corpus (7)

• The 3x+1 Problem: An Annotated Bibliography, II (2000-2009)
• Robust minimality of iterated function systems with two generators
• Kelly Betting with Quantum Payoff: a continuous variable approach
• Generalized Collatz Maps with Almost Bounded Orbits
• Action of Non Abelian Group Generated by Affine Homotheties on R^n
• Semigroups of real functions with dense orbits
• Random interval homeomorphisms