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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Invariant measures for piecewise continuous maps

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Author(s):
Pires, Benito
Total Authors: 1
Document type: Journal article
Source: COMPTES RENDUS MATHEMATIQUE; v. 354, n. 7, p. 717-722, JUL 2016.
Web of Science Citations: 0
Abstract

We say that f : {[}0, 1] -> {[}0, 1] is a piecewise continuous interval map if there exists a partition 0 = x(0) < x(1) < ... < x(d) < x(d+1) = 1 of {[}0, 1] such that f vertical bar((xi-1, xi)) is continuous and the lateral limits w(0)(+) = lim(x -> 0+) f(x), w(d+1)(-) = lim(x -> 1-) f(x), w(i)(-) = lim(x -> xi-) f(x) and w(i)(+) = lim(x -> xi+) f(x) exist for each i. We prove that every piecewise continuous interval map without connections admits an invariant Borel probability measure. We also prove that every injective piecewise continuous interval map with no connections and no periodic orbits is topologically semiconjugate to an interval exchange transformation. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved. (AU)

FAPESP's process: 15/20731-5 - Piecewise contractions defined on Rn
Grantee:Benito Frazao Pires
Support Opportunities: Regular Research Grants