Ergodic polynomials on 2-adic spheres

• Autorzy: Memić N.

Identyfikatory

DOI

10.4064/ba8099-1-2017

• Języki publikacji: EN

Abstrakty

EN

We provide sufficient conditions for invariance, isometricity and ergodicity of polynomials on 2-adic spheres. These conditions are described as relations satisfied by 2-adic coefficients.

Słowa kluczowe

EN

ergodic polynomials; transitive functions; 2-adic spheres

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2017
• Tom: Vol. 65, no. 1
• Strony: 35--44
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Memić N.

• Department of Mathematics, Faculty of Natural Sciences and Mathematics, University of Sarajevo, Zmaja od Bosne 33-35, Sarajevo, Bosnia and Herzegovina

Bibliografia

• [1] V. Anashin, Ergodic transformations in the space of p-adic integers, in: p-Adic Mathematical Physics, AIP Conf. Proc. 826, Amer. Inst. Phys., Melville, NY, 2006, 3-24.
• [2] V. S. Anashin, Uniformly distributed sequences of p-adic integers, Discrete Math. Appl. 12 (2002), 527-590.
• [3] V. Anashin and A. Khrennikov, Applied Algebraic Dynamics, de Gruyter Exp. Math. 49, de Gruyter, Berlin, 2009.
• [4] V. Anashin, A. Khrennikov and E. Yurova, Ergodicity criteria for non-expanding transformations of 2-adic spheres, Discrete Contin. Dynam. Systems 34 (2014), 367-377.
• [5] J. Bryk and C. E. Silva, Measurable dynamics of simple p-adic polynomials, Amer. Math. Monthly 112 (3) (2005), 212-232.
• [6] Z. Coelho and W. Parry, Ergodicity of p-adic multiplications and the distribution of Fibonacci numbers, in: Topology, Ergodic Theory, Real Algebraic Geometry, Amer. Math. Soc. Transl. (2) 202 (2001), 51-70.
• [7] H. Diao and C. E. Silva, Digraph representations of rational functions over the p-adic numbers, p-adic Numbers Ultrametric Anal. Appl. 3 (2011), 23-38.
• [8] F. Durand and F. Paccaut, Minimal polynomial dynamics on the set of 3-adic integers, Bull. London Math. Soc. 41 (2009), 302-314.
• [9] F. Faà di Bruno, Note sur une nouvelle formule de calcul différentiel, Quart. J. Pure Appl. Math. 1 (1857), 359-360.
• [10] M. Gundlach, A. Khrennikov and K.-O. Lindahl, On ergodic behavior of p-adic dynamical systems, Infin. Dimens. Anal. Quantum Probab. Related Topics 4 (2001), 569-577.
• [11] S. Jeong, Toward the ergodicity of p-adic 1-Lipschitz functions represented by the van der Put series, J. Number Theory 133 (2013), 2874-2891.
• [12] A. Khrennikov and E. Yurova, Criteria of measure-preserving for p-adic dynamical systems in terms of the van der Put basis, J. Number Theory 133 (2013), 484-491.
• [13] E. Yurova, On measure-preserving functions over Z3, p-adic Numbers Ultrametric Anal. Appl. 4 (2012), 326-335.
• [14] E. Yurova, The ergodicity of 1-Lipschitz transformations on 2-adic spheres, in: Valuation Theory in Interaction, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2014, 596-599.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).