Existence and properties of p-tupling fixed points

TL;DR

This paper proves the existence of p-tupling fixed points for certain interval and circle maps with arbitrary critical point degree, and explores their properties such as analyticity and behavior at large degrees.

Contribution

It establishes the existence of p-tupling fixed points for maps with arbitrary critical degree and analyzes their key properties.

Findings

Existence of p-tupling fixed points for maps with critical degree r > 1.

Properties like analyticity and univalence of the fixed points.

Behavior of these fixed points as r approaches infinity.

Abstract

We prove the existence of fixed points of p-tupling renormalization operators for interval and circle mappings having a critical point of arbitrary real degree r > 1. Some properties of the resulting maps are studied: analyticity, univalence, behavior as $r$ tends to infinity.