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Dynamics of rational functions with Siegel disks and polynomial semigroups
Koh Katagata
- Iss: 42, pp 17-57
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The article was published on 2009-03-01 and is currently open access. It has received 2 citations till now. The article focuses on the topics: Siegel modular form & Polynomial.read more
Citations
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Book ChapterDOI
Introduction to the Modern Theory of Dynamical Systems: PRINCIPAL CLASSES OF ASYMPTOTIC TOPOLOGICAL INVARIANTS
Anatole Katok,Boris Hasselblatt +1 more
TL;DR: In this paper, the authors focus on identifying important specific properties associated with the asymptotic behavior of smooth dynamical systems, including growth of the numbers of orbits of various kinds and complexity of orbit families, types of recurrence, and statistical behavior of orbits.
Journal ArticleDOI
Dynamics of transcendental entire functions with siegel disks and its applications
TL;DR: In this paper, it was shown that the Siegel disk and its boundary correspond to those of some quadratic polynomial at the level of quasiconformality.
References
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Book
Introduction to the modern theory of dynamical systems
Anatole Katok,Boris Hasselblatt +1 more
TL;DR: In this article, Katok and Mendoza introduced the concept of asymptotic invariants for low-dimensional dynamical systems and their application in local hyperbolic theory.
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.
Book
Lectures on quasiconformal mappings
TL;DR: The Ahlfors Lectures: Acknowledgments Differentiable quasiconformal mappings The general definition Extremal geometric properties Boundary correspondence The mapping theorem Teichmuller spaces Editors' notes.
Journal ArticleDOI
On the dynamics of polynomial-like mappings
Adrien Douady,John H. Hubbard +1 more
TL;DR: In this article, a parametre d'applications de type polynomial is defined and a set of applications of M dans M. Carrottes pour le dessert are presented.
Book ChapterDOI
Introduction to the Modern Theory of Dynamical Systems: PRINCIPAL CLASSES OF ASYMPTOTIC TOPOLOGICAL INVARIANTS
Anatole Katok,Boris Hasselblatt +1 more
TL;DR: In this paper, the authors focus on identifying important specific properties associated with the asymptotic behavior of smooth dynamical systems, including growth of the numbers of orbits of various kinds and complexity of orbit families, types of recurrence, and statistical behavior of orbits.