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We study the behaviour of the iterates of the Chebyshev polynomials of the first kind in p-adic fields. In particular, we determine in the field of complex p-adic numbers for p > 2, the periodic points of the p-th Chebyshev polynomial of the first kind. These periodic points are attractive points. We describe their basin of attraction. The classification of finite field extensions of the field of p-adic numbers ? p , enables one to locate precisely, for any integer ν ≥ 1, the ν-periodic points of T p : they are simple and the nonzero ones lie in the unit circle of the unramified extension of ? p , (p > 2) of degree ν. This generalizes a result, stated by M. Zuber in his PhD thesis, giving the fixed points of T p in the field ? p , (p > 2). As often happens, we consider separately the case p = 2. Also, if the integer n ≥ 2 is not divisible by p, then any fixed point w of T n is indifferent in the field of p-adic complex numbers and we give for p ≥ 3, the p-adic Siegel disc around w. 相似文献
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Karamoko Diarra 《Bulletin of the Brazilian Mathematical Society》2013,44(1):129-154
IsomonodromicdeformationsofFuchsianequationsoforder2onRiemann sphere are parameterized by the solutions of Garnier system. The purpose of this paper is to construct algebraic solutions exotic, i.e. corresponding to deformations of Fuchsian equation with Zariski dense monodromy. Specifically, we classify all the algebraic solutions (complete) exotic constructed by the method of pull-back of Doran-Kitaev: they are deduced from the data isomonodromic deformations pulling back a Fuchsian equation E given by a family of branched coverings ? t . We first introduce the structures and associated orbifoldes underlying Fuchsian equation. This allows us to have are fined version of the Riemann Hurwitz formula that allows us quickly to show that E must be hypergeometric. Then we come to limit the degree of ? and exponents, and finally to Painlevé VI. We explicitly construct one of these solutions. 相似文献
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Bertin Diarra Fana Tangara 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(2):128-135
Let q be a principal unit of the ring of valuation of a complete valued field K, extension of the field of p-adic numbers. Generalizing Mahler basis, K. Conrad has constructed orthonormal basis, depending on q, of the space of continuous functions on the ring of p-adic integers with values in K. Attached to q there are two models of the quantum plane and a model of the quantum Weyl algebra, as algebras of bounded linear operators
on the space of p-adic continuous functions. For q not a root of unit, interesting orthonormal (orthogonal) families of these algebras are exhibited and providing p-adic completion of quantum plane and quantum Weyl algebras.
The text was submitted by the authors in English. 相似文献
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本文研究经典风险模型中破产概率的渐近行为.利用几何和的方法,获得了索赔额的分布属于S(γ).γ〉0。时破产概率的一个局部渐近式.同时.给出了一个具体的数值的例子. 相似文献
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Adelekan Damola S. Ohunakin Olayinka S. Gill Jatinder Atayero Aderemi A. Diarra Charles D. Asuzu Ebube A. 《Journal of Thermal Analysis and Calorimetry》2019,136(6):2439-2448
Journal of Thermal Analysis and Calorimetry - This paper presents an experimental investigation of energy consumption and heat transfer performance characteristics of a safe mass–charge of... 相似文献
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Periodica Mathematica Hungarica - We provide a unique normal form for rank two irregular connections on the Riemann sphere. In fact, we provide a birational model where we introduce apparent... 相似文献
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A.F. Gerday M. Ben Bettaieb L. Duchêne N. Clement H. Diarra A.M. Habraken 《European Journal of Mechanics - A/Solids》2011,30(3):248-255
This article focuses on the numerical modeling of nanoindentation tests performed on the hexagonal α phase of Ti-5553 alloy in order to identify its mechanical behavior. The main goal consists in determining the relative strength of the slip modes in the α phase of Ti-5553. This work was performed using an elastoviscoplastic crystal plasticity-based constitutive law. The difficulties in determining the slip systems that can be activated and their corresponding critical resolved shear stresses (CRSS) are discussed. Numerical predictions are compared to experimental nanoindentation curves. 相似文献