On Various Types of Shadowing for Geometric Lorenz Flows

TL;DR

This paper investigates shadowing properties of Lorenz flows, demonstrating that they lack limit, average, and asymptotic average shadowing properties under certain reparametrization conditions.

Contribution

It establishes the non-existence of various shadowing properties for Lorenz flows with specific reparametrization constraints, advancing understanding of their dynamical complexity.

Findings

Lorenz flows do not have limit shadowing property

Lorenz flows lack average shadowing property

Lorenz flows do not exhibit asymptotic average shadowing property

Abstract

We show that Lorenz flows have neither limit shadowing property nor average shadowing property nor the asymptotic average shadowing property where the reparametrizations related to these concepts relies on the set of increasing homeomorphisms with bounded variation.