Investigation of polynomial differential systems: classification, bifurcations and...
The study of periodic orbits in piecewise continuous differential systems
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Full text | |
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 |