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Piecewise contractions defined on Rn

Abstract

The aim of this proposal is to study the dynamics of piecewise contractions f:K-K defined on a compact convex set K contained in Rn. More precisely, we are interested in findingconditions under which f is asymptotically periodic almost surely, that is, it has finitely many limit cycles whose basins of attraction form a full subset of K. With such study, we intend to generalize many results obtained recently in the unidimensional case. Possible aplications to the understanding of switched server systems and queueing theory are also in the scope of this project. It also embraces the study of the topological dynamics of the Koopman operator C_f:L^p(K)-L^p(K) defined by C_f(\phi)=\phi\circ f, where f is a piecewise contraction of K. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
PIRES, BENITO. Invariant measures for piecewise continuous maps. COMPTES RENDUS MATHEMATIQUE, v. 354, n. 7, p. 717-722, . (15/20731-5)
NOGUEIRA, ARNALDO; PIRES, BENITO; ROSALES, RAFAEL A.. Topological dynamics of piecewise lambda-affine maps. Ergodic Theory and Dynamical Systems, v. 38, n. 5, p. 1876-1893, . (15/20731-5)

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