Existence of attractors for three-dimensional flows
C.A. Morales
TL;DR
This paper establishes the existence of attractors in three-dimensional flows by leveraging recent theorems, advancing the understanding of dynamical systems and their long-term behavior.
Contribution
It provides a new proof of attractor existence in 3D flows using recent theoretical results, connecting previous work with modern developments.
Findings
Proves existence of attractors in 3D flows
Utilizes recent theorems by Crovisier and Yang
Links attractors with singular hyperbolicity
Abstract
We prove the results in [1] using Theorem 1 of the recent paper [2] by Crovisier and Yang. References: [1] Arbieto, A., Rojas, C., Santiago, B., Existence of attractors, homoclinic tangencies and singular-hyperbolicity for flows, arXiv:1308.1734v1 [math.DS] 8 Aug 2013. [2] Crovisier, S., Yang, D., On the density of singular hyperbolic three-dimensional vector fields: a conjecture of Palis, arXiv:1404.5130v1 [math.DS] 21 Apr 2014.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Stability and Controllability of Differential Equations · Advanced Differential Equations and Dynamical Systems