Puiseux series dynamics of quadratic rational maps
TLDR
In this paper, a complete description of the dynamics of quadratic rational maps with coefficients in the completion of the field of formal Puiseux series is given, and a complete analysis of the complete model is given.Abstract:
We give a complete description for the dynamics of quadratic rational maps with coefficients in the completion of the field of formal Puiseux series.read more
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Book ChapterDOI
Dynamics on Berkovich Spaces in Low Dimensions
TL;DR: In this paper, expanded lecture notes for the summer school on Berkovich spaces that took place at the Institut de Mathematiques de Jussieu, Paris, during June 28-July 9, 2010 are presented.
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Puiseux series polynomial dynamics and iteration of complex cubic polynomials
TL;DR: In this article, the authors studied polynomials with coefficients in a field L as dynamical systems where L is any algebraically closed and complete ultrametric field with dense valuation group and characteristic zero residual field.
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Rescaling limits of complex rational maps
TL;DR: In this paper, it was shown that any sequence of rational maps of degree d ≥ 2 has at most 2 d − 2 dynamically distinct rescaling limits which are not postcritically finite.
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Degenerations of Complex Dynamical Systems II: Analytic and Algebraic Stability
Laura DeMarco,Xander Faber +1 more
TL;DR: In this paper, the authors studied the limit of the equilibrium measures for a degenerating 1-parameter family of rational functions on the Riemann sphere, and constructed a convergent countable-state Markov chain that computes the limit measure.
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Dynamics on trees of spheres
TL;DR: The notion of dynamical covers between trees of spheres for which a periodic sphere corresponds to a rescaling limit is introduced and results of Jan Kiwi regarding rescaling limits are recovered.
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.
Book
Spectral Theory and Analytic Geometry over Non-Archimedean Fields
TL;DR: The spectrum of a commutative Banach ring is described in this paper, and the dimension of a Banach algebra is defined in terms of the spectrum of an analytic space.
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Complex Dynamics and Renormalization
TL;DR: In this article, the authors present a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics, including geometric function theory, quasiconformal mappings, and hyperbolic geometry.
Book
Dynamics in One Complex Variable: Introductory Lectures
TL;DR: In this paper, the dynamics of iterated holomorphic mappings from a Riemann surface to itself are studied, focusing on the classical case of rational maps of the Riemannon sphere.
Journal ArticleDOI
Quasiconformal homeomorphisms and dynamics I. Solution of the Fatou-Julia problem on wandering domains
TL;DR: Disclosed is an apparatus for machining the bolster bowl surface, the bolster pocket surfaces, the fulcrum pin hole surface and the bolster gib surfaces of railroad truck bolsters and a locating template is utilized to properly position the bolster on the fixture.