Estimates of the fractal dimension of attractors for autonomous and non-autonomous dynamical systems: applications

• Grant number: 18/10634-0
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2018
• End date: August 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Arthur Cavalcante Cunha
• Supervisor: José A. Langa
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universidad de Sevilla (US), Spain
• Associated to the scholarship: 16/26289-5 - Estimates of the Fractal Dimension of Attractors for Autonomous and Non-Autonomous Dynamical Systems, BP.DR

Abstract

We describe methods to estimate the fractal dimension of attractors for autonomous and non-autonomous dynamical systems in Banach and Hilbert spaces. The main objective in this project is to obtain a comparison (in a broad sense, being that quantitative and/or qualitative) between those two quotas, when both methods can be applied. Such results will allow us to make the better choice for the estimative of the fractal dimension of attractors and also will give us a better refinement in order to use embedding results of these objects into finite-dimensional euclidian spaces. We have as potential application the use of that theory in Partial Differential Equations and Functional Differential Equations. (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)

CUI, HONGYONG; CARVALHO, ALEXANDRE N.; CUNHA, ARTHUR C.; LANGA, JOSE A.. Smoothing and finite-dimensionality of uniform attractors in Banach spaces. Journal of Differential Equations, v. 285, p. 383-428, JUN 5 2021. (18/10997-6, 18/10634-0, 16/26289-5)

CUI, HONGYONG; CUNHA, ARTHUR C.; LANGA, JOSE A.. Finite-Dimensionality of Tempered Random Uniform Attractors. JOURNAL OF NONLINEAR SCIENCE, v. 32, n. 1, FEB 2022. (16/26289-5, 18/10634-0)

CARVALHO, ALEXANDRE N.; CUNHA, ARTHUR C.; LANGA, JOSE A.; ROBINSON, JAMES C.. Finite-dimensional negatively invariant subsets of Banach spaces. Journal of Mathematical Analysis and Applications, v. 509, n. 2, p. 21-pg., 2022-05-15. (16/26289-5, 20/14075-6, 18/10634-0)