| Grant number: | 08/10659-1 |
| Support type: | Scholarships in Brazil - Post-Doctorate |
| Effective date (Start): | May 01, 2009 |
| Effective date (End): | November 30, 2011 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal Investigator: | André Salles de Carvalho |
| Grantee: | Peter Edward Hazard |
| Home Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| Associated research grant: | 06/03829-2 - Dynamic in low dimensions, AP.TEM |
Abstract The renormalization theory for strongly dissipative H\'enon-like mapswas initiated by de Carvalho, Lyubich and Martens in ``Renormalizationin the Henon family I: Universality but Non-Rigidity'' forperiod-doubling combinatorics and by Hazard in ``H\'enon-like Maps andRenormalisation'' for arbitrary stationary combinatorics. In boththese works it was observed that Universality holds in the this twodimensional case, just as in the one-dimensional (unimodal)case. However, it was also observed that, unlike in theone-dimensional case, rigidity fails under the assumption of `tippreservation' and that the invariant Cantor sets for such maps havealmost everywhere unbounded geometry. We wish to continue this studyof infinitely renormalisable maps and their Cantor sets. In particularwe wish to investigate whether infinitely renormalisable H\'enon-likemaps can have bounded geometry Cantor sets and what implications thishas for universality. (AU) | |