S. Shreeram, T. Abhyankar, and . Moh, Embeddings of the line in the plane, J. Reine Angew. Math, vol.276, pp.148-166, 1975.

A. Dimca, Hypersurfaces in C n diffeomorphic to R 4n?2, 1990.

A. Dubouloz, The cylinder over the Koras-Russell cubic threefold has a trivial Makar-Limanov invariant . to appear in Trans. Groups, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00306229

A. Dubouloz and P. Poloni, On a class of Danielewski surfaces in affine 3-space, Journal of Algebra, vol.321, issue.7, 2009.
DOI : 10.1016/j.jalgebra.2008.12.009
URL : https://hal.archives-ouvertes.fr/hal-00019635

G. Freudenburg, Algebraic theory of locally nilpotent derivations, volume 136 of Encyclopaedia of Mathematical Sciences Invariant Theory and Algebraic Transformation Groups, 2006.

G. Freudenburg and L. Moser-jauslin, Embeddings of Danielewski surfaces, Mathematische Zeitschrift, vol.245, issue.4, pp.823-834, 2003.
DOI : 10.1007/s00209-003-0572-5

R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, vol.52, issue.52, 1977.
DOI : 10.1007/978-1-4757-3849-0

. Sh, L. Kaliman, and . Makar-limanov, AK-invariant of affine domains, Affine algebraic geometry, pp.231-255, 2007.

. Sh, M. Kaliman, and . Zaidenberg, Affine modifications and affine hypersurfaces with a very transitive automorphism group. Transform. Groups, pp.53-95, 1999.

S. Kaliman, Extensions of Isomorphisms between Affine Algebraic Subvarieties of k n Automorphisms of k n, Proc. Amer, pp.325-334, 1991.
DOI : 10.2307/2048516

L. Makar-limanov, On the hypersurfacex+x 2y+z 2+t 3=0 in ???4 or a ???4-like threefold which is not C3, Israel Journal of Mathematics, vol.309, issue.2, pp.419-429, 1996.
DOI : 10.1007/BF02937314

L. Makar-limanov, On the group of automorphisms of a surfacex n y=P(z), Israel Journal of Mathematics, vol.326, issue.1, pp.113-123, 2001.
DOI : 10.1007/BF02802499

L. Moser-jauslin and P. Poloni, Plongements d???une famille d???hypersurfaces de Danielewski et certaines actions de \mathbf{C}^+ sur \mathbf{C}^3, Annales de l???institut Fourier, vol.56, issue.5, pp.1567-1581, 2006.
DOI : 10.5802/aif.2220
URL : http://archive.numdam.org/article/AIF_2006__56_5_1567_0.pdf

P. Poloni, Sur les plongements des hypersurfaces de Danielewski, p.6, 2008.
URL : https://hal.archives-ouvertes.fr/tel-00335868

V. Shpilrain and J. Yu, Embeddings of Hypersurfaces in Affine Spaces, Journal of Algebra, vol.239, issue.1, pp.161-173, 2001.
DOI : 10.1006/jabr.2000.8677

V. Srinivas, On the embedding dimension of an affine variety, Mathematische Annalen, vol.30, issue.1, pp.125-132, 1991.
DOI : 10.1007/BF01446563

M. Suzuki, Propri\'et\'es topologiques des polyn\^omes de deux variables complexes, et automorphismes alg\'ebriques de l'espace $C^{2}$, Journal of the Mathematical Society of Japan, vol.26, issue.2, pp.241-257, 1974.
DOI : 10.2969/jmsj/02620241

S. Arno-van-den-essen, S. Maubach, and . Vénéreau, The special automorphism group of R, J. Pure Appl. Algebra, vol.1, issue.2101, pp.141-146, 2007.