A study of dimension theory applied to dynamical system

Author(s)

Alex Pereira da Silva

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2015-03-13

Examining board members

Alexandre Nolasco de Carvalho; Ali Tahzibi; Joachim Weber

• Advisor: Alexandre Nolasco de Carvalho

Abstract

In this work, we study the asymptotic behavior of autonomous dynamical systems supported on the Dimension Theory. More precisely, we understand how fractal dimension finiteness of the global attractor of a semigroup can be used to study the dynamics in finite dimension, without losing information on the dynamics in doing so. For this purpose, the Mañés Theorem plays a decisive role considering the Hausdorff dimension properties and the fractal dimension; thanks to which we managed to find a projection whose restriction to the attractor is an injective application over a finite dimensional space. Besides, we also acknowledge that this projections approach is largely applied to semigroups arrising from differential equations in infinite dimensional Banach spaces. (AU)

• FAPESP's process: 12/23783-8 - A study of dimension theory applied to dynamical systems
• Grantee: Alex Pereira da Silva
• Support Opportunities: Scholarships in Brazil - Master