Infinite sequence on 2-element alphabet as coordinates of points, determines by unimodal maps

TL;DR

This paper explores how infinite sequences over a two-element alphabet can serve as coordinates for points in the unit interval, linking these codings to the dynamics of continuous unimodal maps.

Contribution

It introduces a novel approach connecting symbolic codings with the behavior of unimodal maps, enhancing understanding of their dynamical properties.

Findings

Establishes a correspondence between sequences and points in [0,1]

Analyzes the coding schemes for unimodal map dynamics

Provides insights into the structure of orbits via symbolic sequences

Abstract

We study in this work different $(0, 1)$-codings of points from the unit interval $[0, 1]$ in the relation with the treatment of continuous unimodal maps.