Renormalization in the Henon family, I: universality but non-rigidity
| dc.creator | de Carvalho, A. | |
| dc.creator | Lyubich, M. | |
| dc.creator | Martens, M. | |
| dc.date | 2005-08-24 | |
| dc.date.accessioned | 2026-07-07T05:22:40Z | |
| dc.date.available | 2026-07-07T05:22:40Z | |
| dc.description | In this paper geometric properties of infinitely renormalizable real Hénon-like maps $F$ in $\R^2$ are studied. It is shown that the appropriately defined renormalizations $R^n F$ converge exponentially to the one-dimensional renormalization fixed point. The convergence to one-dimensional systems is at a super-exponential rate controlled by the average Jacobian and a universal function $a(x)$. It is also shown that the attracting Cantor set of such a map has Hausdorff dimension less than 1, but contrary to the one-dimensional intuition, it is not rigid, does not lie on a smooth curve, and generically has unbounded geometry. | |
| dc.description | 42 pages, 5 pictures | |
| dc.identifier | https://arxiv.org/abs/math/0508477 | |
| dc.identifier | http://arxiv.org/abs/math/0508477 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76149 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F25; 37F45 | |
| dc.title | Renormalization in the Henon family, I: universality but non-rigidity | |
| dc.type | text |