Hausdorff dimension and conformal measures of Feigenbaum Julia sets
| dc.creator | Avila, Artur | |
| dc.creator | Lyubich, Mikhail | |
| dc.date | 2004-08-21 | |
| dc.date.accessioned | 2026-07-07T05:11:27Z | |
| dc.date.available | 2026-07-07T05:11:27Z | |
| dc.description | We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the ``hairiness phenomenon'', there exist many Feigenbaum Julia sets $J(f)$ whose Hausdorff dimension is strictly smaller than two. We also prove that for any Feigenbaum Julia set, the Poincaré critical exponent $\de_\crit$ is equal to the hyperbolic dimension $\HD_\hyp(J(f))$. Moreover, if $\area J(f)=0$ then $\HD_\hyp (J(f))=\HD(J(f))$. In the stationary case, the last statement can be reversed: if $\area J(f)> 0$ then $\HD_\hyp (J(f))< 2$. We also give a new construction of conformal measures on $J(f)$ that implies that they exist for any $\de\in [\de_\crit, \infty)$, and analyze their scaling and dissipativity/conservativity properties. | |
| dc.description | Latex, 51 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408290 | |
| dc.identifier | http://arxiv.org/abs/math/0408290 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72246 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F35 | |
| dc.title | Hausdorff dimension and conformal measures of Feigenbaum Julia sets | |
| dc.type | text |