In this thesis, we seek to model the dynamics of violent political revolutions using adaptations of

homogeneous dynamics. We obtain an upper bound for the set of points whose orbit stays away from a complement

This thesis uses methods from hyperbolic dynamics, Riemannian geometry, and analysis on metric

corresponds to chaotic dynamics between the two moons.

integral orbits of mapping class group dynamics on the moduli space, generalizing a classical Diophantine

known results for the Gromov boundary in the case of the contracting boundary. We show that the dynamics

characterization of image information dynamics through introduction of dynamic zoom, the definition and measurement

clustering on multiplex network data. These measures have deep connections to dynamics and we are able to

classical combinatorial dynamics. We also present a dynamical interpretation of a combinatorial bijection

networks to study the evolution of neuronal dynamics in the brains of epileptic mice in the period leading

usefulness in predicting and analyzing the dynamics of wildlife diseases. Statistical modeling implemented

understanding of HCV infection dynamics and treatment response is still limited, restricting our ability to