The tame and the wild automorphisms of polynomial rings in three variables

By I. Shestakov, Ualbai U. Umirbaev. 2003

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Rigidity of Julia sets for Henon type maps (2013, unknown): “[54].”
The discriminant controls automorphism groups of noncommutative algebras (2014, background): “ent derivation ∂ is determined by xi → ( 0 if i < 2m+1, f(x 2 1,...,x 2m)Ω(x ,...,x 2m) if i = 2m+1, and σ = exp(∂). The automorphisms in (1) and (2) are examples of elementary automorphisms – see [SU]. Lemma 5.13. Let Wn and Ωn := Ω(x 1,...,xn) be deﬁned as in Example 5.12. Then xiΩn = (−1)n−1Ωn”
Automorphisms of the Weyl Algebra (2005, background): “Umirbaev [10] have shown that the Nagata automorphism is wild.”
Dynamics on Berkovich Spaces in Low Dimensions (2012, background): “r-dimensional version of the tight tree at innity, and if this space could be used to shine some light on the wild automorphisms of C3, the existence of which was proved by Shestakov and Umirbaev in [SU04]. The log discrepancy used here is a slight variation of the standard notion in algebraic geome”