• Corpus ID: 119147398

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…
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References

SHOWING 1-10 OF 36 REFERENCES
Topological and symbolic dynamics of the doubling map with a hole
This work motivates the study of open dynamical systems corresponding to the doubling map. In particular, the dynamical properties of the attractor of the doubling map when a symmetric, centred open
Topological and symbolic dynamics for hyperbolic systems with holes
• Mathematics
Ergodic Theory and Dynamical Systems
• 2010
Abstract We consider an axiom A diffeomorphism or a Markov map of an interval and the invariant set Ω* of orbits which never falls into a fixed hole. We study various aspects of the symbolic
Essential Dynamics for Lorenz maps on the real line and the Lexicographical World ? ? Partially supp
• Mathematics
• 2006
Abstract In this paper we describe some topological and geometric properties of the set of sequences LW = { ( a , b ) ∈ Σ 0 × Σ 1 ; a ⩽ σ n ( a ) ⩽ b , a ⩽ σ n ( b ) ⩽ b , ∀ n ∈ N } , which
Open circle maps: Small hole asymptotics
We consider escape from chaotic maps through a subset of phase space, the hole. Escape rates are known to be locally constant functions of the hole position and size. In spite of this, for the
Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps
• Mathematics
• 1993
Abstract We study the dynamics and kneading theory of topologically expansive piecewise increasing maps of the interval with a single discontinuity (Lorenz maps). We characterise those maps which are
Zeros of the kneading invariant and topological entropy for Lorenz maps
• Mathematics
• 1996
If is a unimodal map, then its topological entropy is related to the smallest positive zero s of a certain power series (the kneading invariant of f) by . Moreover, it is implicit in the results of
The classification of topologically expansive lorenz maps
• Mathematics
• 1990
We show that topologically expansive Lorenz maps can be described up to topological conjugacy by their kneading invariants. We also give a simple condition on pairs of symbol sequences which is
Topological conjugation of Lorenz maps by β-transformations
Necessary and sufficient conditions for a Lorenz map to be topologically conjugate to a piecewise linear map with constant slope (a β-transformation) are given, first in terms of kneading invariants
Topological and Ergodic properties of symmetric subshifts
The family of symmetric one sided subshifts in two symbols given by a sequence $a$ is studied. We analyse some of their topological properties such as transitivity, the specification property and
Invariant subsets of expanding mappings of the circle
The continuity of Hausdorff dimension of closed invariant subsets K of a C 2 -expanding mapping g of the circle is investigated. If g / K satisfies the specification property then the equilibrium