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Dynamics of piecewise contractions of the interval

Published online by Cambridge University Press:  03 July 2014

ARNALDO NOGUEIRA  and
BENITO PIRES Open the ORCID record for BENITO PIRES [Opens in a new window]
ARNALDO NOGUEIRA
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France email [email protected]
BENITO PIRES
Affiliation:
Departamento de Computação e Matemática, Faculdade de Filosofia, Ciências e Letras, Universidade de São Paulo, 14040-901, Ribeirão Preto - SP, Brazil email [email protected]
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Abstract

We study the long-term behavior of injective piecewise contractions of the interval. We prove that every injective piecewise contraction with $n-1$ discontinuities has at most $n$ periodic orbits and is topologically conjugate to a piecewise linear contraction.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015 , pp. 2198 - 2215
Copyright
© Cambridge University Press, 2014 

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