2025/01/08 by Sogo Murakami, Murakami, Sogo
Engineering · Mathematics · Physics and Astronomy · #37C10 #37C50 (Primary) #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.2501.04294
openalex publication_date 2025/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that every factor map between topological flows preserves the standard shadowing property if it is injective except for a closed orbit that shrinks to a singularity. As an application, we construct a C^∞-flow on a four-dimensional sphere whose nonwandering set contains an attached hyperbolic singularity yet possesses the standard shadowing property. This gives a counterexample to a conjecture given by Arbieto, López, Rego and Sánchez (Math. Annalen 390:417-437).