arXiv:1506.00067 Abstract | arXiv Analytics

arXiv:1506.00067 [math.DS]Abstract References Reviews Resources

Topological dynamics of the doubling map with asymmetrical holes

Published 2015-05-30Version 1

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 topological transitivity and the specification property for such maps.

Comments: 33 pages

Categories: math.DS

Subjects: 37B10, 37C70, 37E05, 68R15

Keywords: doubling map, asymmetrical hole, topological dynamics, topological entropy function, specification property

Related articles: Most relevant | Search more

arXiv:1903.08331 [math.DS] (Published 2019-03-20)

On the specification property and synchronisation of unique $q$-expansions

Rafael Alcaraz Barrera

arXiv:1509.00255 [math.DS] (Published 2015-09-01)

Intrinsic Ergodicity of Open dynamical systems for the doubling map

Rafael Alcaraz Barrera

arXiv:1302.2486 [math.DS] (Published 2013-02-11, updated 2013-09-11)