Geodesic
Automorphisms of affine surfaces.~I
Izvestiya. Mathematics , Tome 9 (1975) no. 3, pp. 493-534.

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We study the group of automorphisms $\operatorname{Aut}(X)$ of an affine surface $X$ which can be made complete by adding a zigzag. This study is based on the computation of the action of $\operatorname{Aut}(X)$ on a certain tree $\Delta_X$ associated with the surface $X$. Our results are used to give a description of forms of the surface $X$ and of algebraic subgroups of $\operatorname{Aut}(X)$. Bibliography: 15 items. 
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M. Kh. Gizatullin; V. I. Danilov. Automorphisms of affine surfaces.~I. Izvestiya. Mathematics , Tome 9 (1975) no. 3, pp. 493-534. http://geodesic.mathdoc.fr/item/IM2_1975_9_3_a4/

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