Mersenne banner
no. 2
On the dynamics of ϕ:x→x p +a in a local field
Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 81-85.

Let K be a local field, a∈K and ϕ:x→x p +a where p denotes the characteristic of the residue field. We prove that the minimal subsets of the dynamical system (K,ϕ) are cycles and describe the cycles of this system.

Published online:
DOI: 10.5802/acirm.38
Classification: 37B99, 11F85
Keywords: Dynamical systems, local fields 
@article{ACIRM_2010__2_2_81_0,
     author = {David Adam and Youssef Fares},
     title = {On the dynamics of $\varphi :x\rightarrow x^p +a$  in a local field},
     journal = {Actes des rencontres du CIRM},
     pages = {81--85},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     doi = {10.5802/acirm.38},
     zbl = {06938586},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.38/}
}
TY  - JOUR
AU  - David Adam
AU  - Youssef Fares
TI  - On the dynamics of $\varphi :x\rightarrow x^p +a$  in a local field
JO  - Actes des rencontres du CIRM
PY  - 2010
SP  - 81
EP  - 85
VL  - 2
IS  - 2
PB  - CIRM
UR  - https://acirm.centre-mersenne.org/articles/10.5802/acirm.38/
UR  - https://zbmath.org/?q=an%3A06938586
UR  - https://doi.org/10.5802/acirm.38
DO  - 10.5802/acirm.38
LA  - en
ID  - ACIRM_2010__2_2_81_0
ER  - 
%0 Journal Article
%A David Adam
%A Youssef Fares
%T On the dynamics of $\varphi :x\rightarrow x^p +a$  in a local field
%J Actes des rencontres du CIRM
%D 2010
%P 81-85
%V 2
%N 2
%I CIRM
%U https://doi.org/10.5802/acirm.38
%R 10.5802/acirm.38
%G en
%F ACIRM_2010__2_2_81_0
David Adam; Youssef Fares. On the dynamics of $\varphi :x\rightarrow x^p +a$  in a local field. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 81-85. doi : 10.5802/acirm.38. https://acirm.centre-mersenne.org/articles/10.5802/acirm.38/

[1] D. Adam and Y. Fares, On two like-affine dynamical systems in a local field, preprint. | DOI | MR | Zbl

[2] A.-H. Fan and Y. Fares, Minimal subsystems of affine dynamics on local fields, Arch. Math. 96 (2011), 423–434. | DOI | MR | Zbl

[3] Y. Fares, Factorial preservation, Arch. Math. 83 (2004), 497–506. | DOI | MR | Zbl

Cited by Sources: