This book investigates the relatively new subject of Arithmetic
Dynamics, which is the study of the number theoretic properties of
algebraic numbers or points under repeated application of a polynomial
or rational map. Classical discrete dynamics is the study of iteration
of functions mapping the complex plane (or real line) to itself.
Arithmetic dynamics is the study of the number-theoretic properties of
rational and algebraic points under repeated application of a polynomial
or rational function. The viewpoint of this book is that many of the
fundamental problems in the theory of Diophantine equations have
dynamical analogs. As is typical in any subject combining Diophantine
problems and geometry, an overarching theme is that at least
qualitatively, the geometry determines the arithmetic.