Chaotic dynamical systems

• Grant number: 18/06916-0
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2018
• End date: August 31, 2020
• 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 first aim of this proposal is to find necessary and sufficient conditions for the occurrence of Li-Yorke chaos in the composition operator $T_f:\varphi\mapsto \varphi\circ f$ acting on $L^p(X,\mathscr{B},\mu)$, where $\mu$ is a $\sigma$-finite measure on the Banach space $X$ and $f:X\to X$ is an injective bimeasurable map. The second aim of this proposal is the construction of switched server systems with Cantor attractors. This proposal also includes the study of suspensions of piecewise contractions with Cantor attractors. (AU)

Scientific publications

(5)

(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. Symbolic dynamics of piecewise contractions. Nonlinearity, v. 32, n. 12, p. 4871-4889, DEC 2019. (18/06916-0)

BERNARDES, N. C., JR.; DARJI, U. B.; PIRES, B.. Li-Yorke chaos for composition operators on L-p-spaces. MONATSHEFTE FUR MATHEMATIK, v. 191, n. 1, p. 23-pg., 2019-10-17. (17/22588-0, 17/19360-8, 18/06916-0)

BERNARDES, JR., N. C.; DARJI, U. B.; PIRES, B.. Li-Yorke chaos for composition operators on L-p-spaces. MONATSHEFTE FUR MATHEMATIK, OCT 2019. (17/22588-0, 17/19360-8, 18/06916-0)

FERNANDES, FILIPE; PIRES, BENITO. A switched server system semiconjugate to a minimal interval exchange. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, v. 31, n. 4, p. 682-708, AUG 2020. (18/06916-0)

DARJI, UDAYAN B.; PIRES, BENITO. CHAOS AND FREQUENT HYPERCYCLICITY FOR COMPOSITION OPERATORS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 64, n. 3, p. 513-531, AUG 2021. (18/06916-0, 17/19360-8, 19/10269-3)