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A study of dimension theory applied to dynamical systems

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


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)

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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.

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