Topological dynamics of linear operators

• Grant number: 17/19360-8
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 01, 2018
• End date: July 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Benito Frazao Pires
• Grantee: Benito Frazao Pires
• Visiting researcher: Udayan Babubhai Darji
• Visiting researcher institution: University of Louisville (UofL), United States
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM

Abstract

This research proposal aims at broadening the scientific collaboration between Visiting Professor Udayan Darji (University of Louisville) and Professor Benito Pires (USP-Ribeirão Preto), through a long-term visit (12 months) of the first researcher. Prior and successful scientific collaboration between the involved researchers (which resulted in a submitted article and another in progress) gives a positive indication of the potential of this proposal. One of the research problems is to characterize the topological dynamics of continuous linear operators (composition operators action on $L^p$-spaces), providing necessary and sufficient conditions for the operator to be Li-Yorke chaotic, Devaney chaotic or frequently hypercyclic. Linear chaos is a research topic that lies at the confluence of multiple areas of mathematics, favoring scientific collaboration between researchers with different expertises: Analysis (Udayan Darji) and Ergodic Theory of Dynamical Systems (Benito Pires). The visiting researcher is full professor at University of Louisville and author of 56 scientific articles, distributed along journals with quite selective policies such as Advances in Mathematics, Transactions of the American Mathematical Society, Proceedings of the American Mathematical Society and Fundamenta Mathematicae. Beyond the main activities described previously, the visiting professor will also interact with professors Ali Messaoudi (UNESP-São José do Rio Preto) and Pedro Levit Kaufmann (UNIFESP). He will give talks at USP-Ribeirão Preto, USP-São Paulo, USP-São Carlos, IBILCE-UNESP, UFSCar and UNIFESP, and give a minicourse on Geometric Measure Theory for students and professors at USP-Ribeirão Preto. (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)

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)

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)

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)