Existence of a Lorenz renormalization fixed point of an arbitrary critical order

TL;DR

This paper proves the existence of a Lorenz renormalization fixed point for a specific non-unimodal map type with any critical order greater than one, advancing the understanding of Lorenz dynamics.

Contribution

It establishes the existence of a fixed point in Lorenz map renormalization for arbitrary critical orders and a specific combinatorial type, extending previous results.

Findings

Fixed point exists for Lorenz maps with arbitrary critical order rho>1

The proof applies to a specific non-unimodal combinatorial type

Advances the theoretical understanding of Lorenz map renormalization

Abstract

We present a proof of the existence of a renormalization fixed point for Lorenz maps of the simplest non-unimodal combinatorial type ({0,1},{1,0,0}), and with a critical point of arbitrary order rho>1.