Examples of wandering domains in p-adic polynomial dynamics
[Exemples des domaines errants dans la dynamique polynôme p-adique]
Comptes Rendus. Mathématique, Tome 335 (2002) no. 7, pp. 615-620.

Soit p>0 un nombre premier. Nous construisons des polynômes p-adiques dans p [z] dont les ensembles de Fatou ont des domaines errants.

For any prime p>0, we contruct p-adic polynomial functions in p [z] whose Fatou sets have wandering domains.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02531-1
Benedetto, Robert L. 1

1 Department of Mathematics, Amherst College, P.O. Box 5000, Amherst, MA 01002, USA
@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] Benedetto, R. p-adic dynamics and Sullivan's No Wandering Domains theorem, Compositio Math., Volume 122 (2000), pp. 281-298

[2] Benedetto, R. 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] Bézivin, J.-P. Sur les points périodiques des applications rationnelles en analyse ultramétrique, Acta Arith., Volume 100 (2001), pp. 63-74

[5] Gouvêa, F. p-adic Numbers. An Introduction, Springer-Verlag, Berlin, 1997

[6] Herman, M.; Yoccoz, J.-C. 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] Hsia, L.-C. Closure of periodic points over a non-Archimedean field, J. London Math. Soc. Ser. 2, Volume 62 (2000), pp. 685-700

[8] Koblitz, N. 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] Serre, J.-P. Corps Locaux, Hermann, Paris, 1968

[13] Sullivan, D. 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 :