Geodesic
Piecewise expanding maps: combinatorics, dynamics and representation of rational numbers
Cristina Serpa1 ; Jorge Buescu1
1 Centro de Matemática e Aplicações Fundamentais, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
ESAIM. Proceedings, Tome 46 (2014), pp. 213-216.

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We establish combinatorial properties of the dynamics of piecewise increasing, continuous, expanding maps of the interval such as description of periodic and pre-periodic points, primitiveness of truncated itineraries and length of pre-periodic itineraries. We include a relation between the dynamics of a family of circle maps and the properties of combinatorial objects as necklaces and words. We identify in a natural way each periodic orbit with an aperiodic necklace. We show the relevance of this combinatorial approach for the representation of rational numbers and for the orbit structure of pre-periodic points.
DOI : 10.1051/proc/201446017

Cristina Serpa 1 ; Jorge Buescu 1

1 Centro de Matemática e Aplicações Fundamentais, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal 
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     author = {Cristina Serpa and Jorge Buescu},
     title = {Piecewise expanding maps: combinatorics, dynamics and representation of rational numbers},
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Cristina Serpa; Jorge Buescu. Piecewise expanding maps: combinatorics, dynamics and representation of rational numbers. ESAIM. Proceedings, Tome 46 (2014), pp. 213-216. doi : 10.1051/proc/201446017. http://geodesic.mathdoc.fr/articles/10.1051/proc/201446017/

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