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  • 1.
    Khrennikov, Andrei
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Criteria of measure-preserving for p-adic dynamical systems in terms of the van der Put basis2013In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 133, no 2, p. 484-491Article in journal (Refereed)
    Abstract [en]

    This paper is devoted to (discrete) p-adic dynamical systems, an important domain of algebraic and arithmetic dynamics. We consider the following open problem from theory of p-adic dynamical systems. Given continuous function f : Z(p) -> Z(p). Let us represent it via special convergent series, namely van der Put series. How can one specify whether this function is measure-preserving or not for an arbitrary p? In this paper, for any prime p, we present a complete description of all compatible measure-preserving functions in the additive form representation. In addition we prove the criterion in terms of coefficients with respect to the van der Put basis determining whether a compatible function f : Z(p) -> Z(p) preserves the Haar measure. (C) 2012 Elsevier Inc. All rights reserved.

  • 2.
    Nordqvist, Jonas
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Characterization of 2-ramified power series2017In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 174, p. 258-273Article in journal (Refereed)
    Abstract [en]

    In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics p. Let g be such a series, then g has a fixed point at the origin and the corresponding lower ramification numbers of g are then, up to a constant, the degree of the first non-linear term of p-power iterates of g. The result is a complete characterization of power series g having ramification numbers of the form 2 ( 1 + p + 
 + p n ) . Furthermore, in proving said characterization we explicitly compute the first significant terms of g at its pth iterate.

  • 3.
    Yurova Axelsson, Ekaterina
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Generalization of Hensel's lemma: Finding the roots of p-adic Lipschitz functions2016In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 158, p. 217-233Article in journal (Refereed)
    Abstract [en]

    In this paper we consider the problem of finding the roots of p-adic functions. In the case, where the function is defined by a polynomial with integer p-adic coefficients, using Hensel's lifting lemma helps us find the roots of the p-adic function.

    We generalize Hensel's lifting lemma for a wider class of p  -adic functions, namely, the functions which satisfy the Lipschitz condition with constant , in particular, the functions of this class may be non-differentiable. The paper also presents an iterative procedure for finding approximate (in p  -adic metric) values of the root of pα-Lipschitz functions, thus generalizing the p-adic analogue of Newton's method for such a class of functions.

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