Recurrence-based characterization of model shadowability in the presence of unstable dimension variability

¹ Universidade Federal do Paraná, Departamento de Física - 81531-980, Curitiba, Paraná, Brazil
² Potsdam Institute for Climate Impact Research - 14412 Potsdam, Germany
³ Research Institute of Intelligent Complex Systems, Fudan University - Shanghai 200433, China
⁴ Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen Aberdeen AB24 3UE, UK
⁵ Universidade Federal do Paraná, CICTI, NCC - Curitiba, Paraná, Brazil

Received: 15 September 2025
Accepted: 15 December 2025

Abstract

Unstable dimension variability is an extreme form of non-hyperbolic behavior, causing severe obstructions to shadowability of numerically generated trajectories of chaotic systems. It has been argued that, in spite of the poor model shadowability of systems with unstable dimension variability, ensembles of chaotic numerical trajectories may still be useful for statistical calculations. The kicked double rotor is a four-dimensional map exhibiting unstable dimension variability for a large parameter interval. By exploring the recurrence properties, we confirm previous claims that, despite the unpredictability of individual trajectories in the kicked double rotor due to unstable dimension variability, statistical measures and recurrence properties remain stable, suggesting their robustness in characterizing the system. While these findings are specific to this system and do not constitute a general proof, a sliding window analysis further confirms the temporal consistency of recurrence measures, supporting their reliability in studying complex chaotic dynamics and encouraging further exploration of their role in hyperchaotic regimes.