Geodesic
Perturbed Dynamical Systems in $\mathfrak p$-Adic Fields
Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 264-272.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $k$ be a $\mathfrak p$-adic field, and let $\mathcal D$ be the class of all discrete dynamical systems defined by polynomials of the kind $h(x)=x+g(x)$, where $g(x)\in k[x]$ is irreducible. Using Krasner's lemma as a tool, we investigate the stability of this class with respect to perturbations of the kind $h_r(x)=h(x)+r(x)$, where $h(x)\in \mathcal D$ and $r(x)\in k[x]$. 
@article{TRSPY_2004_245_a26,
     author = {P.-A. Svensson},
     title = {Perturbed {Dynamical} {Systems} in $\mathfrak p${-Adic} {Fields}},
     journal = {Informatics and Automation},
     pages = {264--272},
     publisher = {mathdoc},
     volume = {245},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a26/}
}
TY  - JOUR
AU  - P.-A. Svensson
TI  - Perturbed Dynamical Systems in $\mathfrak p$-Adic Fields
JO  - Informatics and Automation
PY  - 2004
SP  - 264
EP  - 272
VL  - 245
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a26/
LA  - en
ID  - TRSPY_2004_245_a26
ER  - 
%0 Journal Article
%A P.-A. Svensson
%T Perturbed Dynamical Systems in $\mathfrak p$-Adic Fields
%J Informatics and Automation
%D 2004
%P 264-272
%V 245
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a26/
%G en
%F TRSPY_2004_245_a26
P.-A. Svensson. Perturbed Dynamical Systems in $\mathfrak p$-Adic Fields. Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 264-272. http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a26/

[1] Albeverio S., Tirotstsi B., Khrennikov A. Yu., de Shmedt S., “$p$-Adicheskie dinamicheskie sistemy”, Teor. i mat. fizika, 114:3 (1998), 349–365 | MR | Zbl

[2] Arrowsmith D. K., Vivaldi F., “Geometry of $p$-adic Siegel discs”, Physica D., 71 (1994), 222–236 | DOI | MR | Zbl

[3] Artin E., Algebraic numbers and algebraic functions, Gordon and Breach, New York, 1967 | MR | Zbl

[4] Benedetto R., “Hyperbolic maps of $p$-adic dynamics”, Ergod. Theory and Dyn. Syst., 21 (2001), 1–11 | DOI | MR | Zbl

[5] Cassels J. W. S., Local fields, Cambridge Univ. Press, Cambridge, 1986 | MR

[6] Khrennikov A., $p$-Adic valued distributions in mathematical physics, Kluwer, Dordrecht, 1994 | MR | Zbl

[7] Khrennikov A. Yu., Non-Archimedean analysis: Quantum paradoxes, dynamical systems and biological models, Kluwer, Dordrecht, 1997 | MR | Zbl

[8] {Lindahl K.-O.}, On Markovian properties of the dynamics on attractors of random dynamical systems over the $p$-adic numbers, Repts Växjö Univ. 8, Växjö Univ., 1999

[9] Nilsson M., “Cycles of monomial and perturbated monomial $p$-adic dynamical systems”, Ann. Math. B. Pascal., 7:1 (2000), 37–63 | MR | Zbl

[10] Nilsson M., “Distribution of cycles of monomial $p$-adic dynamical systems”, $p$-Adic functional analysis, Proc. 6th Intern. Conf. (Ioannina, Greece, 2000), Lect. Notes Pure and Appl. Math., 222, M. Dekker, New York, 2001, 233–242 | MR | Zbl

[11] Nyqvist R., Dynamical systems in finite field extensions of $p$-adic numbers, Repts Växjö Univ. 12, Växjö Univ., 1999

[12] Svensson P.-A., “Dynamical systems in unramified or totally ramified extensions of the $p$-adic number field”, Ultrametric functional analysis, Seventh Intern. Conf. on $p$-Adic Functional Analysis (Nijmegen, Netherlands, 2002), eds. W. H. Schikhof, C. Perez-Garcia, A. Escassut, Amer. Math. Soc., Providence, RI, 2003, 405–412 | MR | Zbl