scholarly journals Distribution of postcritically finite polynomials III: Combinatorial continuity

2019 ◽  
Vol 244 (1) ◽  
pp. 17-48 ◽  
Author(s):  
Thomas Gauthier ◽  
Gabriel Vigny
Keyword(s):  
Postcritically Finite

scholarly journals SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS

2013 ◽  
Vol 1 ◽  
Author(s):  
MATTHEW BAKER ◽  
LAURA DE MARCO
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Moduli Space ◽  
Dense Subset ◽  
Rational Curves ◽  
Rational Maps ◽  
Complex Polynomial ◽  
Polynomial Dynamical Systems ◽  
Postcritically Finite ◽  
Cubic Polynomials

AbstractWe study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations, in two settings: (1) rational curves that are polynomially parameterized; and (2) cubic polynomials defined by a given fixed point multiplier. We offer a conjecture on the general form of algebraic subvarieties in the moduli space of rational maps on ${ \mathbb{P} }^{1} $ containing a Zariski-dense subset of postcritically finite maps.

scholarly journals Distribution of postcritically finite polynomials Ⅱ: Speed of convergence

2017 ◽  
Vol 11 (1) ◽  
pp. 57-98 ◽  
Author(s):  
Thomas Gauthier ◽  
◽  
Gabriel Vigny
Keyword(s):  
Speed Of Convergence ◽  
Postcritically Finite

scholarly journals A characterization of postcritically minimal Newton maps of complex exponential functions

2018 ◽  
Vol 39 (10) ◽  
pp. 2855-2880
Author(s):  
KHUDOYOR MAMAYUSUPOV
Keyword(s):  
Exponential Function ◽  
Julia Sets ◽  
Exponential Functions ◽  
Postcritically Finite ◽  
One To One ◽  
Complex Exponential

We obtain a unique, canonical one-to-one correspondence between the space of marked postcritically finite Newton maps of polynomials and the space of postcritically minimal Newton maps of entire maps that take the form $p(z)\exp (q(z))$ for $p(z)$, $q(z)$ polynomials and $\exp (z)$, the complex exponential function. This bijection preserves the dynamics and embedding of Julia sets and is induced by a surgery tool developed by Haïssinsky.

Entropy in dimension one

2014 ◽  
Author(s):  
William P. Thurston
Keyword(s):  
Topological Entropy ◽  
Finite Interval ◽  
Algebraic Integer ◽  
Small Letter ◽  
One Dimensional ◽  
Original Manuscript ◽  
Postcritically Finite ◽  
Perron Number ◽  
One Dimensional Maps ◽  
Dimension One

This chapter studies the topological entropy h of postcritically finite one-dimensional maps and, in particular, the relations between dynamics and arithmetics of eʰ, presenting some constructions for maps with given entropy and characterizing what values of entropy can occur for postcritically finite maps. In particular, the chapter proves: h is the topological entropy of a postcritically finite interval map if and only if h = log λ‎, where λ‎ ≥ 1 is a weak Perron number, i.e., it is an algebraic integer, and λ‎ ≥ ∣λ‎superscript Greek Small Letter Sigma∣ for every Galois conjugate λ‎superscript Greek Small Letter Sigma ∈ C. Unfortunately, the author of this chapter has died before completing this work, hence this chapter contains both the original manuscript as well as a number of notes which clarify many of the points mentioned therein.

scholarly journals On the set of subarcs in some non-postcritically finite dendrites

2019 ◽  
Vol 16 ◽  
pp. 975-982
Author(s):  
N. V. Abrosimov ◽  
M. V. Chanchieva ◽  
A. V. Tetenov
Keyword(s):  
Postcritically Finite
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