Soit p>0 un nombre premier. Nous construisons des polynômes p-adiques dans dont les ensembles de Fatou ont des domaines errants.
For any prime p>0, we contruct p-adic polynomial functions in whose Fatou sets have wandering domains.
Accepté le :
Publié le :
@article{CRMATH_2002__335_7_615_0, author = {Benedetto, Robert L.}, title = {Examples of wandering domains in p-adic polynomial dynamics}, journal = {Comptes Rendus. Math\'ematique}, pages = {615--620}, publisher = {Elsevier}, volume = {335}, number = {7}, year = {2002}, doi = {10.1016/S1631-073X(02)02531-1}, language = {en}, url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02531-1/} }
TY - JOUR AU - Benedetto, Robert L. TI - Examples of wandering domains in p-adic polynomial dynamics JO - Comptes Rendus. Mathématique PY - 2002 SP - 615 EP - 620 VL - 335 IS - 7 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02531-1/ DO - 10.1016/S1631-073X(02)02531-1 LA - en ID - CRMATH_2002__335_7_615_0 ER -
%0 Journal Article %A Benedetto, Robert L. %T Examples of wandering domains in p-adic polynomial dynamics %J Comptes Rendus. Mathématique %D 2002 %P 615-620 %V 335 %N 7 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02531-1/ %R 10.1016/S1631-073X(02)02531-1 %G en %F CRMATH_2002__335_7_615_0
Benedetto, Robert L. Examples of wandering domains in p-adic polynomial dynamics. Comptes Rendus. Mathématique, Tome 335 (2002) no. 7, pp. 615-620. doi : 10.1016/S1631-073X(02)02531-1. http://www.numdam.org/articles/10.1016/S1631-073X(02)02531-1/
[1] p-adic dynamics and Sullivan's No Wandering Domains theorem, Compositio Math., Volume 122 (2000), pp. 281-298
[2] Components and periodic points in non-Archimedean dynamics, Proc. London Math. Soc. (3), Volume 84 (2002), pp. 231-256
[3] R. Benedetto, Wandering domains in non-Archimedean dynamics, in preparation
[4] Sur les points périodiques des applications rationnelles en analyse ultramétrique, Acta Arith., Volume 100 (2001), pp. 63-74
[5] p-adic Numbers. An Introduction, Springer-Verlag, Berlin, 1997
[6] Generalizations of some theorems of small divisors to non-Archimedean fields, Geometric Dynamics, Rio de Janeiro, 1981, Lecture Notes in Math., 1007, Springer-Verlag, Berlin, 1983, pp. 408-447
[7] Closure of periodic points over a non-Archimedean field, J. London Math. Soc. Ser. 2, Volume 62 (2000), pp. 685-700
[8] p-adic Numbers, p-adic Analysis, and Zeta-Functions, Springer-Verlag, New York, 1984
[9] J. Rivera-Letelier, Dynamique des fonctions rationnelles sur des corps locaux, Ph.D. thesis, Université de Paris-Sud, Orsay, 2000
[10] J. Rivera-Letelier, Espace hyperbolique p-adique et dynamique de fonctions rationnelles, Preprint, 2001
[11] J. Rivera-Letelier, Sur la structure des ensembles de Fatou p-adiques, Preprint, 2001
[12] Corps Locaux, Hermann, Paris, 1968
[13] Quasiconformal homeomorphisms and dynamics, I, Solution of the Fatou–Julia problem on wandering domains, Ann. of Math., Volume 122 (1985), pp. 401-418
Cité par Sources :