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Title: Dinàmica simbòlica i aplicacions als sistemes dinàmics
Author: Sallent Martínez, Cristina
Director/Tutor: Fagella Rabionet, Núria
Keywords: Caos (Teoria de sistemes)
Treballs de fi de grau
Funcions de diverses variables complexes
Equacions diferencials ordinàries
Dinàmica topològica
Models matemàtics
Chaotic behavior in systems
Bachelor's thesis
Functions of several complex variables
Ordinary differential equations
Topological dynamics
Mathematical models
Issue Date: 19-Jan-2020
Abstract: [en] Chaos theory is a branch of mathematics focusing on dynamic systems with irregular behavior. Despite being deterministic dynamical systems, their behavior cannot be predicted since small differences in initial conditions can cause the system to evolve very differently. In this paper we will see some examples of very simple dynamical systems but with chaotic dynamics. We will focus mainly on the study of the family $Q_{c}(x)=x^{2}+c$ on the real and complex case. We will talk about symbolic dynamics and topological conjugacy as a useful tool to compare dynamical systems and transfer information from one to another. These two concepts will be used to prove that a dynamical system is chaotic.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Núria Fagella Rabionet
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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