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Dynamical Systems Commons

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Full-Text Articles in Dynamical Systems

Bifurcation And Index Theory With Applications To Nonlinear Differential Equations, Asrafi Yesmin Jan 2025

Bifurcation And Index Theory With Applications To Nonlinear Differential Equations, Asrafi Yesmin

UNF Graduate Theses and Dissertations

This thesis presents a rigorous framework for the study of bifurcation phenomena in nonlinear differential equations. Semigroup theory and index theory are introduced to examine qualitative changes in the solution structures of the nonlinear dynamic system as the parameters vary. The theoretical framework is then applied to several nonlinear differential equations from biology and physics.


The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel Jan 2024

The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …


Bifurcation Levels Of The Integral Manifolds Of The Newtonian N-Body Problem, Hannah G. Havel Jan 2023

Bifurcation Levels Of The Integral Manifolds Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem, first proposed by Isaac Newton, is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It has significance to many areas of science, including physics and computer science, and is crucial in understanding how the universe works. In fact, it was a primary motivation for Newton's development of calculus. An important application of the N-body problem is within celestial mechanics and involves how planets and other celestial bodies move with mutual gravitational attraction. It is important in developing how satellites behave in space using complicated …