Piecewise contractions defined on Rn

• Grant number: 15/20731-5
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2016
• End date: January 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Benito Frazao Pires
• Grantee: Benito Frazao Pires
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

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)

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, JUL 2016. (15/20731-5)

NOGUEIRA, ARNALDO; PIRES, BENITO; ROSALES, RAFAEL A.. Topological dynamics of piecewise lambda-affine maps. Ergodic Theory and Dynamical Systems, v. 38, p. 18-pg., 2018-08-01. (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, AUG 2018. (15/20731-5)