A numerical method for constructing the hyperbolic structure of complex Henon mappings

dc.creatorHruska, Suzanne Lynch
dc.date2004-05-31
dc.date2005-12-22
dc.date.accessioned2026-07-07T12:40:03Z
dc.date.available2026-07-07T12:40:03Z
dc.descriptionFor complex parameters a,c, we consider the Henon mapping H_{a,c}: C^2 -> C^2 given by (x,y) -> (x^2 +c -ay, x), and its Julia set, J. In this paper, we describe a rigorous computer program for attempting to construct a cone field in the tangent bundle over J, which is preserved by DH, and a continuous norm in which DH (and DH^{-1}) uniformly expands the cones (and their complements). We show a consequence of a successful construction is a proof that H is hyperbolic on J. We give several new examples of hyperbolic maps, produced with our computer program, Hypatia, which implements our methods.
dc.description25 pages. 5 figures. Submitted
dc.identifierhttps://arxiv.org/abs/math/0406004
dc.identifierhttp://arxiv.org/abs/math/0406004
dc.identifierFound. Comput. Math. 6 (2006), no. 4, 427--455.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219328
dc.subjectDynamical Systems
dc.subject32H50, 37F15, 37C50, 37-04, 37F50
dc.titleA numerical method for constructing the hyperbolic structure of complex Henon mappings
dc.typetext

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