Discrete Holomorphic Local Dynamical Systems

52 Marco Abate
[CD] Coman, D., Dabija, M.: On the dynamics of some diffeomorphisms of C 2 near parabolic
fixed points. Houston J. Math. 24, 85–96 (1998)
[Cr1] Cremer, H.: Zum Zentrumproblem. Math. Ann. 98, 151–163 (1927)
[Cr2] Cremer, H.: Über die Häufigkeit der Nichtzentren. Math. Ann. 115, 573–580 (1938)
[D1] Degli Innocenti, F.: Holomorphic dynamics near germs of singular curves. Math. Z. 251,
943–958 (2005)
[D2] Degli Innocenti, F.: On the relations between discrete and continuous dynamics in C 2 .
Ph.D. Thesis, Università di Pisa (2007)
[DG] DeLatte, D., Gramchev, T.: Biholomorphic maps with linear parts having Jordan blocks:
linearization and resonance type phenomena. Math. Phys. El. J. 8, 1–27 (2002)
[Di] Di Giuseppe, P.: Topological classification of holomorphic, semi-hyperbolic germs in
quasi-absence of resonances. Math. Ann. 334, 609–625 (2006)
[DH] Douady, A., Hubbard, J.H.: On the dynamics of polynomial-like mappings. Ann. Sc. Éc.
Norm. Sup. 18, 287–343 (1985)
[Du] Dulac, H.: Recherches sur les points singuliers des équationes différentielles. J. Éc. Polytech.
IX, 1–125 (1904)
[É1] Écalle, J.: Théorie itérative: introduction àlathéorie des invariants holomorphes. J.
Math. Pures Appl. 54, 183–258 (1975)
[É2] Écalle, J.: Les fonctions résurgentes. Tome I: Les algèbres de fonctions résurgentes,
Prépublications Math. Orsay 81-05, Université de Paris-Sud, Orsay, 1981. Download
site: http://www.math.u-psud.fr/ ˜ biblio/numerisation/docs/
E ECALLE 81 05/pdf/E ECALLE 81 05.pdf
[É3] Écalle, J.: Les fonctions résurgentes. Tome II: Les fonctions résurgentes appliquées à
l’itération, Prépublications Math. Orsay 81-06, Université de Paris-Sud, Orsay, 1981.
Download site: http://www.math.u-psud.fr/ ˜ biblio/numerisation/
docs/E ECALLE 81 06/pdf/E ECALLE 81 06.pdf
[É4] Écalle, J.: Les fonctions résurgentes. Tome III: L’équation du pont et la classification
analytique des objects locaux, Prépublications Math. Orsay 85-05, Université deParis-
Sud, Orsay, 1985. Download site: http://www.math.u-psud.fr/ ˜ biblio/
numerisation/docs/E ECALLE 85 05/pdf/E ECALLE 85 05.pdf
[É5] Écalle, J.: Iteration and analytic classification of local diffeomorphisms of C ν ,inIteration
theory and its functional equations. Lecture Notes in Mathematics, vol. 1163,
pp. 41–48. Springer-Verlag, Berlin (1985)
[ÉV] Écalle, J., Vallet, B.: Correction and linearization of resonant vector fields and diffeomorphisms.
Math. Z. 229, 249–318 (1998)
[FHY] Fathi, A., Herman, M., Yoccoz, J.-C.: A proof of Pesin’s stable manifold theorem, in
Geometric Dynamics. Lecture Notes in Mathematics, vol. 1007, pp. 177–216. Springer
Verlag, Berlin (1983)
[F1] Fatou, P.: Sur les équations fonctionnelles, I. Bull. Soc. Math. France, 47, 161–271
(1919)
[F2] Fatou, P.: Sur les équations fonctionnelles, II. Bull. Soc. Math. France, 48, 33–94 (1920a)
[F3] Fatou, P.: Sur les équations fonctionnelles, III. Bull. Soc. Math. France, 48, 208–314
(1920b)
[F4] Fatou, P.: Substitutions analytiques et équations fonctionnelles à deux variables. Ann.
Sci. École Norm. Sup. 40, 67–142 (1924)
[Fa] Favre, C.: Classification of 2-dimensional contracting rigid germs and Kato surfaces. I.
J. Math. Pures Appl. 79, 475–514 (2000)
[FJ1] Favre, C., Jonsson, M.: The valuative tree. Lecture Notes in Mathematics, vol. 1853.
Springer Verlag, Berlin (2004)
[FJ2] Favre, C., Jonsson, M.: Eigenvaluations. Ann. Sci. École Norm. Sup. 40, 309–349 (2007)
[GS] Gelfreich, V., Sauzin, D.: Borel summation and splitting of separatrices for the Hénon
map. Ann. Inst. Fourier Grenoble, 51, 513–567 (2001)
[GH] Griffiths, P., Harris, J.: Principles of algebraic geometry. Wyley, New York (1978)
[G1] Grobman, D.M.: Homeomorphism of systems of differential equations. Dokl. Akad.
Nauk. USSR, 128, 880–881 (1959)