Reference : Limit functions of discrete dynamical systems
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Limit functions of discrete dynamical systems
Beise, Peter [> >]
Meyrath, Thierry mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit]
Müller, Jürgen [University of Trier > Fachbereich IV - Mathematik]
Conformal Geometry and Dynamics
American Mathematical Society
Yes (verified by ORBilu)
[en] Julia set ; Limit set ; Siegel disk ; Universality
[en] In the theory of dynamical systems, the notion of ω-limit sets of points is classical. In this paper, the existence of limit functions on subsets of the underlying space is treated. It is shown that in the case of topologically mixing systems on appropriate metric spaces (X, d), the existence of at least one limit function on a compact subset A of X implies the existence of plenty of them on many supersets of A. On the other hand, such sets necessarily have to be small in various respects. The results for general discrete systems are applied in the case of Julia sets of rational functions and in particular in the case of the existence of Siegel disks.

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