Cristina Serpa_Combinatorics and symbolic dynamics for

Cristina Serpa_Combinatorics and symbolic dynamics for

Combinatorics and symbolic dynamics for
piecewise expanding maps
Cristina Serpa∗, Jorge Buescu†
Faculty of Sciences of the University of Lisbon and CMAF
Abstract
Using topological conjugacies we establish properties of the dynamics
of piecewise increasing, continuous and expanding functions (such as periodic and pre-periodic points, primitiveness of truncated itineraries, length
of pre-periodic itineraries). We include a relation between the dynamics
of a family of circle maps and the properties of such combinatorial objects
as necklaces and words. We identify in a natural way each periodic orbit
with an aperiodic necklace, and with a Lyndon word.
Keywords: piecewise monotone, periodic point, necklace, primitive
word, Lyndon word
AMS subject classification: 37E15, 37E05, 37E10.
∗ Postal address: Departamento de Matemática, Ed. C6, Campo Grande, 1749-006 Lisboa
Portugal, Tel: 00351 936626152, E-mail: [email protected]
† Postal address: Departamento de Matemática, Ed. C6, Campo Grande, 1749-006 Lisboa
Portugal, Tel: 00351 2175100293, E-mail: [email protected]
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