Let be a local field, and where denotes the characteristic of the residue field. We prove that the minimal subsets of the dynamical system are cycles and describe the cycles of this system.
@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}, language = {en}, url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.38/} }
Adam, David; Fares, Youssef. On the dynamics of $\varphi :x\rightarrow x^p +a$ in a local field. Actes des rencontres du CIRM, Tome 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.
[2] A.-H. Fan and Y. Fares, Minimal subsystems of affine dynamics on local fields, Arch. Math. 96 (2011), 423–434.
[3] Y. Fares, Factorial preservation, Arch. Math. 83 (2004), 497–506.