Periodic attractors of perturbed one dimensional maps

TL;DR

This paper explores the number of periodic attractors near a given one-dimensional map, introducing new tools for uniform cross-ratio distortion estimates around maps with degenerate critical points.

Contribution

It develops novel methods for estimating distortion in neighborhoods of maps with degenerate critical points, advancing understanding of periodic attractors.

Findings

Established bounds on the number of periodic attractors near a given map.

Developed new techniques for cross-ratio distortion estimates.

Enhanced analytical tools for maps with degenerate critical points.

Abstract

In this paper we investigate how many periodic attractors maps in a small neighbourhood of a given map can have. For this purpose we develop new tools which help to make uniform cross-ratio distortion estimates in a neighbourhood of a map with degenerate critical points.