Dynamics and number theory long were quite dinstinct fields of mathematics. Recently, however, progress has been made in the application of number theory to dynamics. This text seeks to elucidate a...Show moreDynamics and number theory long were quite dinstinct fields of mathematics. Recently, however, progress has been made in the application of number theory to dynamics. This text seeks to elucidate a small bit of this progress. The focus will be on the special case of discrete dynamical systems, which consist of a set X associated with a map φ : X → X. As in this text we will mainly consider X = P n (Q), the first section serves as an introduction to projective geometry. To provide the reader with some intuition, it starts out with P 1 (C) and eventually switches attention to P n (Q). The second section introduces the basic notions of discrete dynamics. In the third section, ‘height functions’ are defined. These are functions of the form h : P n (Q) → R, and they serve as the main tool in applying number theory to dynamics. As we restrict attention to projective spaces over Q, their definitions can remain quite simple; when working over an arbitrary number field K, one runs into the problem that the ring of integers of K may not be a principal ideal domain, making the definition of h substantially more complicated. For this, refer to [1]. After having defined them, some important properties of the height functions are derived. Section 4 then utilizes these properties to quickly derive some interesting theorems relating arithmetic to discrete dynamical systems.Show less