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Articles 1 - 3 of 3
Full-Text Articles in Dynamical Systems
Complex Dimensions Of 100 Different Sierpinski Carpet Modifications, Gregory Parker Leathrum
Complex Dimensions Of 100 Different Sierpinski Carpet Modifications, Gregory Parker Leathrum
Master's Theses
We used Dr. M. L. Lapidus's Fractal Zeta Functions to analyze the complex fractal dimensions of 100 different modifications of the Sierpinski Carpet fractal construction. We will showcase the theorems that made calculations easier, as well as Desmos tools that helped in classifying the different fractals and computing their complex dimensions. We will also showcase all 100 of the Sierpinski Carpet modifications and their complex dimensions.
Dynamical Systems And Matching Symmetry In Beta-Expansions, Karl Zieber
Dynamical Systems And Matching Symmetry In Beta-Expansions, Karl Zieber
Master's Theses
Symbolic dynamics, and in particular β-expansions, are a ubiquitous tool in studying more complicated dynamical systems. Applications include number theory, fractals, information theory, and data storage.
In this thesis we will explore the basics of dynamical systems with a special focus on topological dynamics. We then examine symbolic dynamics and β-transformations through the lens of sequence spaces. We discuss observations from recent literature about how matching (the property that the itinerary of 0 and 1 coincide after some number of iterations) is linked to when Tβ,⍺ generates a subshift of finite type. We prove the set of ⍺ in …
The Long-Run Effects Of Tropical Cyclones On Infant Mortality, Isabel Miranda
The Long-Run Effects Of Tropical Cyclones On Infant Mortality, Isabel Miranda
Master's Theses
In the United States alone, each tropical cyclone causes an average of $14.6 billion worth of damages. In addition to the destruction of physical infrastructure, natural disasters also negatively impact human capital formation. These losses are often more difficult to observe, and therefore, are over looked when quantifying the true costs of natural disasters. One particular effect is an increase in infant mortality rates, an important indicator of a country’s general socioeconomic level. This paper utilizes a model created by Anttila-Hughes and Hsiang, that takes advantage of annual variation in tropical cyclones using annual spatial average maximum wind speeds and …