# Topological dynamics of the doubling map with asymmetrical holes

@article{Barrera2015TopologicalDO, title={Topological dynamics of the doubling map with asymmetrical holes}, author={Rafael Alcaraz Barrera}, journal={arXiv: Dynamical Systems}, year={2015} }

We study the dynamics of the attractor of the doubling map with an asymmetrical hole by associating to each hole an element of the lexicographic world. A description of the topological entropy function is given. We show that the set of parameters $(a,b)$ such that the dynamics of the mentioned attractor corresponds to a subshift of finite type is open and dense. Using the connections between this family of open dynamical systems, intermediate $\beta$-expansions and Lorenz maps we study the… Expand

#### 2 Citations

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We give sufficient conditions for intervals $(a,b)$ such that the associated open dynamical system for the doubling map is intrinsically ergodic. We also show that the set of parameters $(a,b) \in… Expand

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Let $T_{k}$ be the expanding map of $[0,1)$ defined by $T_{k}(x) = k x\ \text{mod 1}$, where $k\geq 2$ is an integer. Given $0\leq a<b\leq 1$, let $\mathcal{W}_{k}(a,b)=\{x\in [0,1)\ \vert \… Expand

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