Geometric Lorenz flows with historic behavior

TL;DR

This paper demonstrates that in the geometric Lorenz flow, a residual set of initial states leads to orbits exhibiting historic behavior, highlighting the prevalence of such complex dynamics.

Contribution

It establishes that the set of initial conditions producing historic orbits is residual within a trapping region of the geometric Lorenz flow.

Findings

Residual set of initial states with historic behavior

Historic orbits are prevalent in the geometric Lorenz flow

Provides insight into complex dynamical behaviors in Lorenz systems

Abstract

We will show that, in the the geometric Lorenz flow, the set of initial states which give rise to orbits with historic behavior is residual in a trapping region.