Well-Approximable Points for Julia Sets with Parabolic and Critical Points
Stratmann, Bernd O. ; Urbanski, Mariusz ; Zinsmeister, Michel
HAL, hal-00079375 / Harvested from HAL
Text on HAL
In this paper we consider rational functions $f\colon \oc \to \oc$ with parabolic and critical points contained in their Julia sets $J(f)$ such that $$ \sum_{n=1}^\infty|(f^n)'(f(c))|^{-1}<\infty $$ for each critical point $c \in J(f)$. We calculate the Hausdorff dimensions of subsets of $J(f)$ consisting of elements $z$ for which $$ \inf\{\dist(f^n(z),\Crit(f)):\, n\ge 0\}>0 $$ and which are well-approximable by backward iterates of the parabolic periodic points of $f$.
Publié le : 2001-07-05
Classification:  Diophantine analysis,  Rational functions,  critical phenomena,  ergodic theory,  fractal geometry,  Diophantine analysis.,  37A45, 30C99, 30D40, 11K36.,  [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 
@article{hal-00079375,
     author = {Stratmann, Bernd O. and Urbanski, Mariusz and Zinsmeister, Michel},
     title = {Well-Approximable Points for Julia Sets with Parabolic and Critical Points},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00079375}
}

Stratmann, Bernd O.; Urbanski, Mariusz; Zinsmeister, Michel. Well-Approximable Points for Julia Sets with Parabolic and Critical Points. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00079375/