A numerical method for constructing the hyperbolic structure of complex Henon mappings
| dc.creator | Hruska, Suzanne Lynch | |
| dc.date | 2004-05-31 | |
| dc.date | 2005-12-22 | |
| dc.date.accessioned | 2026-07-07T12:40:03Z | |
| dc.date.available | 2026-07-07T12:40:03Z | |
| dc.description | For 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.description | 25 pages. 5 figures. Submitted | |
| dc.identifier | https://arxiv.org/abs/math/0406004 | |
| dc.identifier | http://arxiv.org/abs/math/0406004 | |
| dc.identifier | Found. Comput. Math. 6 (2006), no. 4, 427--455. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219328 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 32H50, 37F15, 37C50, 37-04, 37F50 | |
| dc.title | A numerical method for constructing the hyperbolic structure of complex Henon mappings | |
| dc.type | text |