A note on finite-time Lyapunov dimension of the Rossler attractor

TL;DR

This paper verifies Eden's conjecture on the maximum local Lyapunov dimension of the Rössler attractor by numerically computing finite-time local Lyapunov dimensions on the attractor and unstable periodic orbits using Pyragas control.

Contribution

It provides the first numerical verification of Eden's conjecture for the Rössler system using advanced control and computation techniques.

Findings

Confirmed Eden's conjecture for the Rössler attractor

Computed finite-time Lyapunov dimensions on attractor and unstable periodic orbits

Applied Pyragas time-delay feedback control for orbit computation

Abstract

For the R\"ossler system we verify Eden's conjecture on the maximum of local Lyapunov dimension. We compute numerically finite-time local Lyapunov dimensions on the R\"ossler attractor and embedded unstable periodic orbits. The UPO computation is done by Pyragas time-delay feedback control technique.