2006/09/29 by Han Peters, Liz Vivas, Liz Raquel Vivas +4
Mathematics · Physics and Astronomy · #32H02 #32H50 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.CV #math.DS #msc:32H02 #msc:32H50
paper · pdf · doi:10.48550/arxiv.math/0610001
11 pages
arxiv created 2006/09/29 · openalex publication_date 2006/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study toplogical properties of attracting sets for automorphisms of ℂk. Our main result is that a generic volume preserving automorphism has a hyperbolic fixed point with a dense stable manifold. We prove the same result for volume preserving maps tangent to the identity. On the other hand, we show that an attracting set can only contain a neighborhood of the fixed point if the fixed point is an attracting fixed point. We will see that the latter does not hold in the non-autonomous setting.