Skip to main content
SpringerLink
Log in

Two-periodic dynamics in finite extensions of the p-adic number field

  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

We investigate 2-periodic points of a certain class of dynamical systems defined over the field of p-adic numbers. We determine the topological properties of these points and the nature of the smallest finite extension in which the periodic points reside.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. S. Anashin, “Uniformly Distributed Sequences of p-adic Integers,” Diskretn. Mat. 14(4), 3–64 (2002) [Discrete Math. Appl. 12, 527–590 (2002)].

    MathSciNet  Google Scholar 

  2. R. L. Benedetto, “Hyperbolic Maps in p-adic Dynamics,” Ergodic Theory Dyn. Syst. 21, 1–11 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  3. D. Ford, S. Pauli, and X.-F. Roblot, “A Fast Algorithm for Polynomial Factorization over ℚp,” J. Théor. Nombres Bord. 14(1), 151–169 (2002).

    MATH  MathSciNet  Google Scholar 

  4. A. Yu. Khrennikov, “p-Adic Discrete Dynamical Systems and Their Applications in Physics and Cognitive Sciences,” Russ. J. Math. Phys. 11(1), 45–70 (2004).

    MATH  MathSciNet  Google Scholar 

  5. A. Yu. Khrennikov and M. Nilsson, p-Adic Deterministic and Random Dynamics (Kluwer, Dordrecht, 2004).

    MATH  Google Scholar 

  6. A. Yu. Khrennikov and P.-A. Svensson, “Attracting Fixed Points of Polynomial Dynamical Systems in Fields of p-adic Numbers,” Izv. Ross. Akad. Nauk, Ser. Mat. 71(4), 103–114 (2007) [Izv. Math. 71, 753–764 (2007)].

    MathSciNet  Google Scholar 

  7. R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, rev. ed. (Cambridge Univ. Press, Cambridge, 1994).

    MATH  Google Scholar 

  8. K.-O. Lindahl, “On Markovian Properties of the Dynamics on Attractors of Random Dynamical Systems over the p-adic Numbers,” MASDA Rep. (Växjö Univ., 1999).

  9. J. Lubin, “Nonarchimedean Dynamical Systems,” Compos. Math. 94, 321–346 (1994).

    MATH  MathSciNet  Google Scholar 

  10. M. Nilsson, “Distribution of Cycles of Monomial p-adic Dynamical Systems,” in p-Adic Functional Analysis (M. Dekker, New York, 2001), Lect. Notes Pure Appl. Math. 222, pp. 233–242.

    Google Scholar 

  11. R. Nyqvist, “Algebraic Dynamical Systems, Analytical Results and Numerical Simulations,” Ph.D. Thesis (Växjö Univ., Växjö, 2007).

    Google Scholar 

  12. P.-A. Svensson, “Dynamical Systems in Unramified or Totally Ramified Extensions of the p-adic Number Field,” in Ultrametric Functional Analysis: Proc. Seventh Int. Conf. on p-adic Functional Analysis, Ed. by W. H. Schikhof, C. Perez-Garcia, and A. Escassut (Am. Math. Soc., Providence, RI, 2003), Contemp. Math. 319, pp. 405–412.

    Google Scholar 

  13. P.-A. Svensson, “Dynamical Systems in Local Fields of Characteristic Zero,” Ph.D. Thesis (Växjö Univ., Växjö, 2004).

    Google Scholar 

  14. P.-A. Svensson, “Dynamical Systems in Unramified or Totally Ramified Extensions of a p-adic Field,” Izv. Ross. Akad. Nauk, Ser. Mat. 69(6), 211–218 (2005) [Izv. Math. 69, 1279–1287 (2005)].

    MathSciNet  Google Scholar 

  15. P.-A. Svensson, “On 2-Periodic Points of p-adic Dynamical Systems Whose Fixed Points Are Zeros of an Eisenstein Polynomial,” MSI Rep. No. 07112 (Växjö Univ., 2007).

  16. P.-A. Svensson and R. Nyqvist, “On the Number of Equivalence Classes of Attracting Dynamical Systems,” MSI Rep. No. 06118 (Växjö Univ., 2006).

  17. D. Verstegen, “p-Adic Dynamical Systems,” in Number Theory and Physics (Springer, Berlin, 1990), Springer Proc. Phys. 47, pp. 235–242.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Systems Engineering, Växjö University, SE-351 95, Växjö, Sweden

    Per-Anders Svensson

Authors
  1. Per-Anders Svensson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Per-Anders Svensson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Svensson, PA. Two-periodic dynamics in finite extensions of the p-adic number field. Proc. Steklov Inst. Math. 265, 235–241 (2009). https://doi.org/10.1134/S0081543809020229

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543809020229

Keywords

Search

Navigation