On the dynamics of ϕ : x x p + a in a local field

David Adam; Youssef Fares

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 2, page 81-85
  • ISSN: 2105-0597

Abstract

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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.

How to cite

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Adam, David, and Fares, Youssef. "On the dynamics of $\varphi :x\rightarrow x^p +a$ in a local field." Actes des rencontres du CIRM 2.2 (2010): 81-85. <http://eudml.org/doc/196288>.

@article{Adam2010,
abstract = {Let $K$ be a local field, $a \in K$ and $\varphi :x\rightarrow x^p +a$ 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.},
author = {Adam, David, Fares, Youssef},
journal = {Actes des rencontres du CIRM},
keywords = {Dynamical systems; local fields},
language = {eng},
number = {2},
pages = {81-85},
publisher = {CIRM},
title = {On the dynamics of $\varphi :x\rightarrow x^p +a$ in a local field},
url = {http://eudml.org/doc/196288},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Adam, David
AU - Fares, Youssef
TI - On the dynamics of $\varphi :x\rightarrow x^p +a$ in a local field
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 81
EP - 85
AB - Let $K$ be a local field, $a \in K$ and $\varphi :x\rightarrow x^p +a$ 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.
LA - eng
KW - Dynamical systems; local fields
UR - http://eudml.org/doc/196288
ER -

References

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  1. D. Adam and Y. Fares, On two like-affine dynamical systems in a local field, preprint. Zbl1273.37046
  2. A.-H. Fan and Y. Fares, Minimal subsystems of affine dynamics on local fields, Arch. Math.96 (2011), 423–434. Zbl1214.11134MR2805346
  3. Y. Fares, Factorial preservation, Arch. Math.83 (2004), 497–506. Zbl1073.13011MR2105326

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