On the shifts of stable and unstable manifolds of a hyperbolic cycle under perturbation

2024/07/08 by W. Wei, Wei, Wenyin, Jiankun Hua +4
Earth and Planetary Sciences · #39B52 #76W05 #78M30 #Aquatic and Environmental Studies #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Plasma Physics (physics.plasm-ph) #Primary: 37D10 #Secondary: 39A33

paper · pdf · doi:10.48550/arxiv.2407.06430

openalex publication_date 2024/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control, are computable with minimal effort using functional derivatives by considering the entire system as an argument. The shifts of homoclinic and heteroclinic orbits, as the intersections of these manifolds, are readily calculated by analyzing the movements of the intersection points.

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