Topological and Symbolic dynamics of the doubling map with a hole

  • Rafael Alcaraz Barrera

Student thesis: Phd


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.
Date of Award1 Aug 2015
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorNikita Sidorov (Supervisor) & Richard Hewitt (Supervisor)


  • intrinsic ergodicity
  • Open dynamical systems
  • doubling map
  • topological transitivity
  • specification property
  • beta expansions

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