P-adic dynamics

Summary

$p$-adic dynamics studies the iteration of maps defined over the $p$-adic numbers and their extensions, such as rational functions and convergent power series. It is a discrete-time dynamical system theory in which distances come from a non-Archimedean absolute value. The strong triangle inequality makes the behaviour of orbits very different from the real or complex case. It is a basic tool of arithmetic dynamics, where $p$-adic methods control orbits of points over number fields.