Attracting basins of volume preserving automorphisms of $\mathbb{C}^k$

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dc.creatorPeters, Han
dc.creatorVivas, Liz Raquel
dc.creatorWold, Erlend Fornæss
dc.date2006-09-29
dc.date.accessioned2026-07-07T07:28:31Z
dc.date.available2026-07-07T07:28:31Z
dc.descriptionWe study toplogical properties of attracting sets for automorphisms of $\mathbb{C}^k$. 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.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0610001
dc.identifierhttp://arxiv.org/abs/math/0610001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117757
dc.subjectComplex Variables
dc.subjectDynamical Systems
dc.subject32H02, 32H50
dc.titleAttracting basins of volume preserving automorphisms of $\mathbb{C}^k$
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