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- Title
ATTRACTING BASINS OF VOLUME PRESERVING AUTOMORPHISMS OF ℂ<sup>k</sup>.
- Authors
Peters, Han; Vivas, Liz Raquel; Wold, Erlend Fornæss
- Abstract
We study topological 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. On the other hand, we show that an attracting set can only contain a neighborhood of the fixed point if it is an attracting fixed point. We will see that the latter does not hold in the non-autonomous setting.
- Subjects
AUTOMORPHISMS; TOPOLOGICAL spaces; MANIFOLDS (Mathematics); HYPERBOLIC spaces; DYNAMICS; ATTRACTORS (Mathematics); VOLUMETRIC analysis
- Publication
International Journal of Mathematics, 2008, Vol 19, Issue 7, p801
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X08004893