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Title: Topological and symbolic dynamics of the doubling map with a hole
Author: Alcaraz Barrera, Rafael
ISNI:       0000 0004 5360 2136
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2014
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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 interval is removed are studied. Using the arithmetical properties of the binary expansion of the points on the boundary of the removed interval, we study properties such as topological transitivity, the specification property and intrinsic ergodicity. The properties of the function that associates to each hole $(a,b)$ the topological entropy of the attractor of the considered dynamical system are also shown. For these purposes, a subshift corresponding to an element of the lexicographic world is associated to each attractor and the mentioned properties are studied symbolically.
Supervisor: Not available Sponsor: CONACYT, Mexico
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Open dynamical systems ; doubling map ; topological transitivity ; specification property ; intrinsic ergodicity ; beta expansions