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Iteration of entire functions
TLDR
In this article, the results discussed in the lectures at the CIMPA school in Kathmandu in November 2014 were discussed and the proofs of the results were given. But some references to the literature where proofs can be found are given.Abstract:
These notes contain the results discussed in the lectures at the CIMPA school in Kathmandu in November 2014. They contain only some of the proofs, but some references to the literature where proofs can be found are given.read more
Citations
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Julia and escaping set spiders' webs of positive area
TL;DR: In this paper, the authors studied the dynamics of a collection of families of transcendental entire functions which generalises the well-known exponential and cosine families and showed that for functions in many of these families the Julia set, the escaping set and the fast escaping set are all spiders' webs of positive area.
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Hollow quasi-Fatou components of quasiregular maps
TL;DR: In this paper, the authors define a quasi-Fatou component of a quasiregular map as a connected component of the complement of the Julia set, and show that if U is bounded, then U has many properties in common with a multiply connected Fatou component, whereas U is completely invariant and has no unbounded boundary components.
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Dynamical sets whose union with infinity is connected
TL;DR: In this article, it was shown that the escaping set of the bounded orbit set and the bungee set can also be connected, and sufficient conditions for these sets to be connected.
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Chaotic dynamics of a quasiregular sine mapping
TL;DR: In this paper, the authors studied the iterative behaviour of a quasiregular mapping that is an analogue of a sine function and proved that the periodic points of S form a dense subset of.
Posted Content
Escaping set and Julia set of transcendental semigroups
TL;DR: In this article, the dynamics of semigroups of transcendental entire functions using Fatou-Julia theory are discussed and a condition for the complete invariance of escaping set and Julia set of a semigroup is provided.
References
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Book
Dynamics in one complex variable
TL;DR: In this article, the dynamics of iterated holomorphic mappings from a Riemann surface to itself are studied, focusing on the classical case of rational maps of the RiemANN sphere.
Journal ArticleDOI
Iteration of meromorphic functions
TL;DR: In this paper, the authors describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions, and some aspects where the transcendental case is analogous to the rational case are treated rather briefly here.
On Meromorphic Functions. I
TL;DR: In this article, the applications of homogeneous differential polynomials to the Nevanlinna theory of meromorphic functions in the finite complex plane have been given, and some generalizations by these polynomial coefficients have been shown.