A point is normal for almost all maps βx+α mod 1 or generalized β-transformations

DOI10.1017/S0143385708000874zbMath1184.37034arXiv0806.2922OpenAlexW2158526896MaRDI QIDQ3645388

Beáta Faller, Charles-Edouard Pfister

Publication date: 18 November 2009

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.2922

zbMATH Keywords

probability measuresergodic measures\(\beta\)-transformations\(\mu\)-normal orbitsmappings of the unit interval

Mathematics Subject Classification ID

Dynamical systems involving maps of the interval (37E05)

Related Items (10)

On co-\(\sigma\)-porosity of the parameters with dense critical orbits for skew tent maps and matching on generalised \(\beta\)-transformations ⋮ Density of periodic measures and large deviation principle for generalised mod one transformations ⋮ Matching for generalised \(\beta\)-transformations ⋮ BETA ENCODERS: SYMBOLIC DYNAMICS AND ELECTRONIC IMPLEMENTATION ⋮ Equilibrium state for one-dimensional Lorenz-like expanding maps ⋮ Circularly invariant uniformizable probability measures for linear transformations ⋮ Unique equilibrium states for some intermediate beta transformations ⋮ Natural extensions for \(p\)-adic \(\beta\)-shifts and other scaling maps ⋮ On the specification property and synchronization of uniqueq-expansions ⋮ Law of iterated logarithm and invariance principle for one-parameter families of interval maps

Cites Work

• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy
• Explicit construction of invariant measures for a class of continuous state Markov processes
• Fubini foiled: Katok's paradoxical example in measure theory
• Maximal measures for simple piecewise monotonic transformations
• Representations for real numbers and their ergodic properties
• Periodic points and homoclinic classes
• Symbolic dynamics for $\beta$-shifts and self-normal numbers
• Topological Entropy for Noncompact Sets
• The trajectory of the turning point is dense for almost all tent maps
• On the topological entropy of saturated sets
• Representations for real numbers

This page was built for publication: A point is normal for almost all maps βx+α mod 1 or generalized β-transformations