Complex Horseshoes and the Dynamics of Mappings of Two Complex Variables
| dc.creator | Oberste-Vorth, Ralph W. | |
| dc.date | 2005-07-04 | |
| dc.date | 2005-07-06 | |
| dc.date.accessioned | 2026-07-07T05:21:23Z | |
| dc.date.available | 2026-07-07T05:21:23Z | |
| dc.description | In this study, a theory analogous to both the theories of polynomial-like mappings and Smale's real horseshoes is developed for the study of the dynamics of mappings of two complex variables. In partial analogy with polynomials in a single variable there are the Hénon mappings in two variables as well as higher dimensional analogues. From polynomial-like mappings, Hénon-like and quasi-Hénon-like mappings are defined following this analogy. A special form of the latter is the complex horseshoe. The major results about the real horseshoes of Smale remain true in the complex setting. In particular: (1) Trapping fields of cones(which are sectors in the real case) in the tangent spaces can be defined and used to find horseshoes. (2) The dynamics of a horseshoe is that of the two-sided shift on the symbol space on some number of symbols which depends on the type of the horseshoe. (3) Transverse intersections of the stable and unstable manifolds of a hyperbolic periodic point guarantee the existence of horseshoes. | |
| dc.description | 26 pages, PhD thesis with addendum | |
| dc.identifier | https://arxiv.org/abs/math/0507073 | |
| dc.identifier | http://arxiv.org/abs/math/0507073 | |
| dc.identifier | Cornell University 1987 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75671 | |
| dc.subject | Dynamical Systems | |
| dc.title | Complex Horseshoes and the Dynamics of Mappings of Two Complex Variables | |
| dc.type | text |