A study of dimension theory applied to dynamical systems

• Grant number: 12/23783-8
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2013
• End date: February 28, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Alex Pereira da Silva
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The aim of this project is to study embeddings of global attractors of semiflows into finite-dimensional euclidean spaces. More specifically, we wish to give conditions under which we can ensure that we can "map" a global attractor injectively onto a subset of an euclidean space, so you can ensure that the asymptotic dynamics of our semigroup (which can be defined in an infinite dimensional Banach space), in fact, occurs in a finite-dimensional space.To this end, we will study the concepts of topological dimension, Hausdorff dimension and fractal dimension in metric spaces and also methods to obtain estimates of these quantities. Such methods are based on the spectral decomposition of linear operators and the construction of exponential attractors for semigroups. (AU)

Academic Publications

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

SILVA, Alex Pereira da. A study of dimension theory applied to dynamical system. 2015. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.