| 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)
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