Hensel's Lemma, Backward Dynamics and p-adic Approximations

TL;DR

This paper explores backward dynamics over p-adic integers, utilizing inverse limit theory and Hensel's lemma to construct backward iterations of polynomials through p-adic congruences.

Contribution

It introduces a framework combining inverse limit theory and Hensel's lemma for analyzing backward dynamics in p-adic settings.

Findings

Backward iterations are constructed via solving congruences modulo p^n.

Hensel's lemma is effectively used for lifting solutions in p-adic polynomial equations.

Inverse limit theory provides a suitable framework for backward dynamics over p-adic integers.

Abstract

The problem of backward dynamics over the ring of p-adic integers is studied. It is shown that Inverse Limit Theory provides the right framework. Backward iterations of a polynomial with p-adic integer coefficients are constructed by solving congruences modulo powers of p, which inturn are solved by Hensel's lifting lemma.