2007/06/16 by Yi Song, Stephen P. Banks · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Attractor #Biology #Chaotic #Combinatorics #Computer science #Dissipative system #Genus #Invariant (physics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Periodic orbits #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Topology (electrical circuits) #Zoology #math.DS #msc:37B35 #msc:37D45
paper · pdf · doi:10.1142/s0218127408020173
published in International Journal of Bifurcation and Chaos 18(01), 109-119 (World Scientific) · 19 pages with 20 figures, AMS La-TeX, to be published in International Journal of Bifurcation and Chaos
arxiv created 2007/06/16 · openalex publication_date 2008/01/01 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins, 2004] and give conditions under which these invariant sets are not homeomorphic to a circle individually, which implies the existence of chaotic behavior. This is achieved by studying the appearance of inversely unstable solutions within each invariant set.