# The -transformation with a hole at 0

@article{Kalle2019TheW, title={The -transformation with a hole at 0}, author={Charlene Kalle and Derong Kong and Niels Langeveld and Wenxia Li}, journal={Ergodic Theory and Dynamical Systems}, year={2019} }

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#### 4 Citations

Two bifurcation sets arising from the beta transformation with a hole at 0

- Mathematics
- 2019

Given $\beta\in(1,2],$ the $\beta$-transformation $T_\beta: x\mapsto \beta x\pmod 1$ on the circle $[0, 1)$ with a hole $[0, t)$ was investigated by Kalle et al.~(2019). They described the set-valued… Expand

Pointwise densities of homogeneous Cantor measure and critical values

- Physics, Mathematics
- 2020

Let N ⩾ 2 and ρ ∈ (0, 1/N 2]. The homogenous Cantor set E is the self-similar set generated by the iterated function system fi(x)=ρx+i(1−ρ)N−1:i=0,1,…,N−1. Let s = dim H E be the Hausdorff dimension… Expand

The bifurcation set as a topological invariant for one-dimensional dynamics

- Physics, Mathematics
- 2019

For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of (some… Expand

Generalized Fibonacci numbers and extreme value laws for the Rényi map

- Mathematics
- 2020

In this paper we prove an extreme value law for a stochastic process obtained by iterating the Renyi map. Haiman (2018) derived a recursion formula for the Lebesgue measure of threshold exceedance… Expand

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Letˇ > 1 be a real number. LetTˇ denote theˇ-transformation on Œ0; 1 . A cylinder of order n is a set of real numbers in Œ0; 1 having the same first n digits in their ˇ-expansion. A cylinder is… Expand