scholarly journals Univalent polynomials and Hubbard trees

2021 ◽  
pp. 1
Author(s):  
Kirill Lazebnik ◽  
Nikolai G. Makarov ◽  
Sabyasachi Mukherjee
Keyword(s):  
Hubbard Trees

External Angles and Hubbard Trees

1986 ◽  
pp. 63-92 ◽  
Author(s):  
Heinz-Otto Peitgen ◽  
Peter H. Richter
Keyword(s):  
Hubbard Trees

scholarly journals Existence of quadratic Hubbard trees

2009 ◽  
Vol 202 (3) ◽  
pp. 251-279 ◽  
Author(s):  
Henk Bruin ◽  
Alexandra Kaffl ◽  
Dierk Schleicher
Keyword(s):  
Hubbard Trees

scholarly journals Hubbard trees

2010 ◽  
Vol 208 (3) ◽  
pp. 193-248 ◽  
Author(s):  
Alfredo Poirier
Keyword(s):  
Hubbard Trees

Hubbard forests

2011 ◽  
Vol 33 (1) ◽  
pp. 303-317 ◽  
Author(s):  
ALFREDO POIRIER
Keyword(s):  
Finite Union ◽  
Complex Numbers ◽  
Polynomial Maps ◽  
Postcritically Finite ◽  
Proper Maps ◽  
Hubbard Trees

AbstractThe theory of Hubbard trees provides an effective classification of nonlinear postcritically finite polynomial maps in ℂ. This note extends the classification to maps from a finite union of copies of ℂ to itself. Holomorphic proper maps on a finite union of copies of ℂ which are postcritically finite and nowhere linear can be characterized by a ‘forest’ made up of one tree for each copy of the set of complex numbers.

scholarly journals Homotopy Hubbard trees for post-singularly finite exponential maps

2021 ◽  
pp. 1-46
Author(s):  
DAVID PFRANG ◽  
MICHAEL ROTHGANG ◽  
DIERK SCHLEICHER
Keyword(s):  
Entire Functions ◽  
Characterization Theorem ◽  
Rational Maps ◽  
Topological Characterization ◽  
Exponential Maps ◽  
The Family ◽  
Transcendental Entire Functions ◽  
Traditional Sense ◽  
Polynomial Dynamics ◽  
Hubbard Trees

Abstract We extend the concept of a Hubbard tree, well established and useful in the theory of polynomial dynamics, to the dynamics of transcendental entire functions. We show that Hubbard trees in the strict traditional sense, as invariant compact trees embedded in $\mathbb {C}$ , do not exist even for post-singularly finite exponential maps; the difficulty lies in the existence of asymptotic values. We therefore introduce the concept of a homotopy Hubbard tree that takes care of these difficulties. Specifically for the family of exponential maps, we show that every post-singularly finite map has a homotopy Hubbard tree that is unique up to homotopy, and that post-singularly finite exponential maps can be classified in terms of homotopy Hubbard trees, using a transcendental analogue of Thurston’s topological characterization theorem of rational maps.

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