Generalised golden ratios over integer alphabets
S Baker - arXiv preprint arXiv:1210.8397, 2012 - arxiv.org
It is a well known result that for $\beta\in (1,\frac {1+\sqrt {5}}{2}) $ and $ x\in (0,\frac {1}{\beta-
1}) $ there exists uncountably many $(\epsilon_ {i}) _ {i= 1}^{\infty}\in {0, 1}^{\mathbb {N}} …
1}) $ there exists uncountably many $(\epsilon_ {i}) _ {i= 1}^{\infty}\in {0, 1}^{\mathbb {N}} …
The random continued fraction transformation
C Kalle, T Kempton, E Verbitskiy - Nonlinearity, 2017 - iopscience.iop.org
We introduce a random dynamical system related to continued fraction expansions. It uses
random combinations of the Gauss map and the Rényi (or backwards) continued fraction …
random combinations of the Gauss map and the Rényi (or backwards) continued fraction …
On a family of self-affine sets: topology, uniqueness, simultaneous expansions
KG Hare, N Sidorov - Ergodic Theory and Dynamical Systems, 2017 - cambridge.org
On a family of self-affine sets: Topology, uniqueness, simultaneous expansions Page 1 Ergod.
Th. & Dynam. Sys. (2017), 37, 193–227 doi:10.1017/etds.2015.41 c Cambridge University …
Th. & Dynam. Sys. (2017), 37, 193–227 doi:10.1017/etds.2015.41 c Cambridge University …
On the invariant density of the random β-transformation
T Kempton - Acta Mathematica Hungarica, 2014 - Springer
We construct a Lebesgue measure preserving natural extension of a skew product system
related to the random β-transformation K β. This allows us to give a formula for the density of …
related to the random β-transformation K β. This allows us to give a formula for the density of …
[图书][B] Overlapping iterated function systems from the perspective of Metric Number Theory
S Baker - 2023 - ams.org
In this paper we develop a new approach for studying overlapping iterated function systems.
This approach is inspired by a famous result due to Khintchine from Diophantine …
This approach is inspired by a famous result due to Khintchine from Diophantine …
Local dimensions for the random beta-transformation
K Dajani, C Kalle - arXiv preprint arXiv:1211.0454, 2012 - arxiv.org
The random beta-transformation K is isomorphic to a full shift. This relation gives an invariant
measure for K that yields the Bernoulli convolution by projection. We study the local …
measure for K that yields the Bernoulli convolution by projection. We study the local …
The growth rate and dimension theory of beta-expansions
S Baker - arXiv preprint arXiv:1208.6195, 2012 - arxiv.org
In a recent paper of Feng and Sidorov they show that for $\beta\in (1,\frac {1+\sqrt {5}}{2}) $
the set of $\beta $-expansions grows exponentially for every $ x\in (0,\frac {1}{\beta-1}) $. In …
the set of $\beta $-expansions grows exponentially for every $ x\in (0,\frac {1}{\beta-1}) $. In …
Approximation properties of -expansions
S Baker - arXiv preprint arXiv:1409.2744, 2014 - arxiv.org
Let $\beta\in (1, 2) $ and $ x\in [0,\frac {1}{\beta-1}] $. We call a sequence $(\epsilon_ {i}) _
{i= 1}^\infty\in\{0, 1\}^{\mathbb {N}} $ a $\beta $-expansion for $ x $ if $ x=\sum_ {i …
{i= 1}^\infty\in\{0, 1\}^{\mathbb {N}} $ a $\beta $-expansion for $ x $ if $ x=\sum_ {i …
Overlapping iterated function systems from the perspective of metric number theory
S Baker - arXiv preprint arXiv:1901.07875, 2019 - arxiv.org
In this paper we develop a new approach for studying overlapping iterated function systems.
This approach is inspired by a famous result due to Khintchine from Diophantine …
This approach is inspired by a famous result due to Khintchine from Diophantine …