BookDOI
Iteration of Rational Functions
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This article is published in American Mathematical Monthly.The article was published on 1991-01-01. It has received 972 citations till now. The article focuses on the topics: Elliptic rational functions & Rational function.read more
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Bloch’s Principle
TL;DR: A heuristic principle attributed to Andre Bloch is that a family of holomorphic functions is likely to be normal if there are no non-constant entire functions with this property.
Journal ArticleDOI
Local dynamics of uniformly quasiregular mappings
TL;DR: In this article, the local dynamics of uniformly quasiregular mappings are investigated, and it is shown that there is no quasiconformal analogue of the Leau-Fatou linearization of parabolic dynamics.
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When do two rational functions have the same Julia set
Genadi Levin,Feliks Przytycki +1 more
TL;DR: In this article, it was shown that non-exceptional rational functions f and g on the Riemann sphere have the same measure of maximal entropy iff there exist iterates F of f and G of g and natural numbers M, N such that (*) (G-1oG)oGM=(F- 1oF)o FN.
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Invariant curves for birational surface maps
TL;DR: In this paper, the authors classify invariant curves for birational surface maps that are expanding on cohomology and show that there is an associated invariant meromorphic two-form.
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On the Julia set of analytic self-maps of the punctured plane
TL;DR: In this paper, it was shown that a non-constant and non-linear entire function can be found in the Julia set of a self-map if and only if e is a member of the set of g.