A switched server system semiconjugate to a minimal interval exchange

Autor(es)

Fernandes, Filipe ^[1] ; Pires, Benito ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

^[2] Univ Sao Paulo, Fac Filosofia Ciencias & Letras, Dept Comp & Matemat, BR-14040901 Ribeirao Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: EUROPEAN JOURNAL OF APPLIED MATHEMATICS; v. 31, n. 4, p. 682-708, AUG 2020.
• Citações Web of Science: 0

Resumo

Switched server systems are mathematical models of manufacturing, traffic and queueing systems that have being studied since the early 1990s. In particular, it is known that typically the dynamics of such systems is asymptotically periodic: each orbit of the system converges to one of its finitely many limit cycles. In this article, we provide an explicit example of a switched server system with exotic behaviour: each orbit of the system converges to the same Cantor attractor. To accomplish this goal, we bring together recent advances in the understanding of the topological dynamics of piecewise contractions and interval exchange transformations (IETs) with flips. The ultimate result is a switched server system whose Poincare map is semiconjugate to a minimal and uniquely ergodic JET with flips. (AU)

• Processo FAPESP: 18/06916-0 - Sistemas dinâmicos caóticos
• Beneficiário: Benito Frazao Pires
• Modalidade de apoio: Auxílio à Pesquisa - Regular