Behaviour of Hensel perturbations of p-adic monomial dynamical systems

摘要

In the framework of non-Archimedean (p-adic) analysis we study cyclic behaviour of polynomial discrete dynamical systems (iterations of polynomial maps). One of the main tools of our investigation is Hensel's lemma (a p-adic analogue of Newton's method). Our considerations will lead to formulas for the number cycles of a specific length and for the total number of cycles. We will also study the distribution of cycles in the different p-adic fields.