One-dimensional non-wandering sets

One-Dimensional Fibers of Rigid Subanalytic Sets

Let K be an algebraically closed eld of any characteristic, complete with respect to the non-trivial ultrametric absolute value jj : K ! R +. By R denote the valuation ring of K, and by } its maximal ideal. We work within the class of subanalytic sets deened in L2], but our results here also hold for the strongly subanalytic sets introduced in S] as well as for those subanalytic sets considered...

Non-rectifiable Limit Sets of Dimension One

Wandering Fatou Components and Algebraic Julia Sets

We study the dynamics of polynomials with coefficients in a nonArchimedean field L, where L is the completion of an algebraic closure of the field of formal Laurent series. We prove that every wandering Fatou component is contained in the basin of a periodic orbit. We give a dynamical characterization of polynomials having algebraic Julia sets. More precisely, we establish that a polynomial wit...

Non-hyperbolic One-dimensional Invariant Sets with a Countably Infinite Collection of Inhomogeneities

In this paper we examine the structure of countable closed invariant sets under a dynamical system on a compact metric space. We are motivated by a desire to understand the possible structures of inhomogeneities in one-dimensional non-hyperbolic sets (inverse limits of finite graphs) particularly when those inhomogeneities form a countable set. All of the previous literature regarding the colle...

Faster Algorithms for Computing Distances between One-Dimensional Point Sets

Let S and T be two finite sets of points on the real line with |S| + |T | = n and |S| > |T |. We consider two distance measures between S and T that have applications in music information retrieval and computational biology: the surjection distance and the link distance. The former is called the restriction scaffold assignment problem in computational biology, and assigns each point of S to a p...