hénon maps
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2022 ◽  
Vol 155 ◽  
pp. 111732
Author(s):  
Aleksandra V. Tutueva ◽  
Lazaros Moysis ◽  
Vyacheslav G. Rybin ◽  
Ekaterina E. Kopets ◽  
Christos Volos ◽  
...  
Keyword(s):  


2021 ◽  
pp. 1-16
Author(s):  
ANNA MIRIAM BENINI ◽  
ALBERTO SARACCO ◽  
MICHELA ZEDDA

Abstract We construct automorphisms of ${\mathbb C}^2$ , and more precisely transcendental Hénon maps, with an invariant escaping Fatou component which has exactly two distinct limit functions, both of (generic) rank one. We also prove a general growth lemma for the norm of points in orbits belonging to invariant escaping Fatou components for automorphisms of the form $F(z,w)=(g(z,w),z)$ with $g(z,w):{\mathbb C}^2\rightarrow {\mathbb C}$ holomorphic.





2021 ◽  
Vol 389 ◽  
pp. 107900
Author(s):  
Michael Yampolsky ◽  
Jonguk Yang


Author(s):  
Seiya Amoh ◽  
Xu Zhang ◽  
Guanrong Chen ◽  
Tetsushi Ueta






2021 ◽  
Vol 207 (2) ◽  
pp. 572-578
Author(s):  
S. Anastassiou
Keyword(s):  


2021 ◽  
Vol 64 (1) ◽  
pp. 1-28
Author(s):  
N. I. Shepherd-Barron

An effective lower bound on the entropy of some explicit quadratic plane Cremona transformations is given. The motivation is that such transformations (Hénon maps, or Feistel ciphers) are used in symmetric key cryptography. Moreover, a hyperbolic plane Cremona transformation g is rigid, in the sense of [5], and under further explicit conditions some power of g is tight.



2021 ◽  
Vol 17 (0) ◽  
pp. 465
Author(s):  
Leandro Arosio ◽  
Anna Miriam Benini ◽  
John Erik Fornæss ◽  
Han Peters

<p style='text-indent:20px;'>Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family of transcendental Hénon maps offers the potential of combining ideas from transcendental dynamics in one variable and the dynamics of polynomial Hénon maps in two. Here we show that these maps all have infinite topological and measure theoretic entropy. The proof also implies the existence of infinitely many periodic orbits of any order greater than two.</p>



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