Estimates of the Fractal Dimension of Attractors for Autonomous and Non-Autonomous Dynamical Systems

• Grant number: 16/26289-5
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2017
• End date: July 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Arthur Cavalcante Cunha
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 18/10634-0 - Estimates of the fractal dimension of attractors for autonomous and non-autonomous dynamical systems: applications, BE.EP.DR

Abstract

We describe the methods used to find estimates of fractal dimension for attractors of autonomous and non-autonomous problems in Banach and Hilbert spaces. The main goal is obtain a comparative (in a broad sense, being that quantitative and/or qualitative) between these two quotas, when both the methods can be applied. Such results will allow us to make the better choice for the estimative of the fractal dimension for attractors and also will give us a better refinement in a way to use embedding results about these objects in finite-dimensional spaces. We have as potentials applications the use of that theory in Partial Differential Equations and Functional Differential Equations.

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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CUNHA, Arthur Cavalcante. Finite-dimensionality of attractors for dynamical systems with applications: deterministic and random settings. 2021. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.