Elliptic Curves and Discrete Dynamical Systems

Abstract

This paper gives an introduction to elliptic curves and discrete dynamical systems. It lays out the foundations of the theory of elliptic curves, along with important concepts like torsion points and isogenies, and makes heavy use of the John Cremona Database of Elliptic Curves. For dynamical systems, this paper gives an introduction to them, along with concepts like (in)stability, periodicity, and Lattès maps.