Actes des rencontres du CIRM

Let $K$ be a local field, $a\in K$ and $\varphi :x\to x^p+a$ where $p$ denotes the characteristic of the residue field. We prove that the minimal subsets of the dynamical system $(K,\varphi )$ are cycles and describe the cycles of this system.

Published online : 2011-10-20
DOI : https://doi.org/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},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     pages = {81-85},
     doi = {10.5802/acirm.38},
     language = {en},
     url = {https://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_81_0}
}

Adam, David; Fares, Youssef. 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/item/ACIRM_2010__2_2_81_0/