Abstract
Let U be an invariant stable domain of a rational function R and z 0 ∈ ∂ U a weakly repelling fixed point of R. Assuming a “local surjective condition”, which is obviously satisfied in the case of a completely invariant domain U, we show that zq is an accessible boundary point of U. This generalizes theorems of several authors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bearden, A. F., Iteration of Rational Functions, Springer 1991
Carleson, L., Gamelin, T. W., Complex Dynamics, Springer 1992
Douady, A., Hubbard, J. H., Études dynamique des polynômes complexes, I & II, Publications Mathématiques d’Orsay (1984/85)
Eremenko, A. E., Levin, G. M., Periodic Points of Polynomials, Ukrainian Mathematical Journal, 41 (1989), 1258–1262
Petersen, C. L., On the Pommerenke-Levin-Yoccoz Inequality, Ergodic Theory & Dynamical Systems 13 (1993), 785–806
Pommerenke, C., Uniformly Perfect Sets and the Poincaré Metric, Archiv Mathematik 32 (1979), 192–199
Przytycki, F., Accessibility of Typical Points for Invariant Measures of Positive Lyapunov Exponents for Iterations of Holomorphic Maps, Fundamenta Mathematicae 144 (1994), 259–278
Schmidt, W., Fixpunkte im Rand stabiler Gebiete, Dissertation Universität Dortmund (1996)
Steinmetz, N., Rational Iteration, de Gruyter 1993
Tsuji, M., Potential Theory in Modern Function Theory, Maruzen 1959
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schmidt, W. Accessible Fixed Points on the Boundary of Stable Domains. Results. Math. 32, 115–120 (1997). https://doi.org/10.1007/BF03322531
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03322531