Periodicity on discrete dynamical systems generated by a class of rational mappings

Abstract

We address the problem of global periodicity in discrete dynamical systems generated by rational maps in or . Our main results show that for a wide family of such maps, this problem may be reduced to the analysis of a related matrix equation. We use this fact to estimate the number of possible minimal periods in globally periodic maps of this class when all the involved coefficients are rational.

Keywords:

• Global periodicity
• Discrete dynamical system
• Periodic point
• Rational map
• Euler's phi-function

Keywords:

• 39B12
• 39A11
• 39B42

Acknowledgements

The authors thank Professors Armengol Gasull and Javier Majadas for useful discussions, and the referee for his/her interesting remarks. This work has been partially supported by M.E.C. (Spain) and FEDER, under grant MTM2004-06652-C03-02.

Notes

^† [email protected].

Additional information

Notes on contributors

Ignacio Bajo

† † [email protected].