Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity Theorems for H\'{e}non maps-II   The purpose of this note is to explore further the rigidity properties of
H\'{e}non maps from arXiv:1806.08189. For instance, we show that if $H$ and $F$
are H\'{e}non maps with the same Green measure ($\mu_H=\mu_F$), or the same
filled Julia set ($K_H=K_F$), or the same Green function ($G_H=G_F$), then
$H^2$ and $F^2$ have to commute. This, in turn, gives that $H$ and $F$ have the
same non-escaping sets. Further we prove that, either of the association of a
H\'{e}non map $H$ to its Green measure $\mu_H$ or to its filled Julia set $K_H$
or to its Green function $G_H$ is locally injective.

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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th