BookDOI
Iteration of Rational Functions
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This article is published in American Mathematical Monthly.The article was published on 1991-01-01. It has received 972 citations till now. The article focuses on the topics: Elliptic rational functions & Rational function.read more
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Sur la compacité des ensembles de Julia des polynômes p-adiques
TL;DR: The compactness of the Julia set of p-adic polynomials was studied in this article for rational functions of degree ≥ 2 with complex coefficients, and it was shown that if one replaces a rational function with a field ℚ p (completion of an algebraic closure of the field of the padic numbers), then one can define also a Julia set for a rational functions with padic coefficients. But as ℂ p is not locally compact, it may or may not be compact.
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Small denominators in complex p-adic dynamics
TL;DR: In this paper, the problem of small denominators in the field of complex p-adic numbers C p was studied, and it was shown that the radius of convergence for conjugate maps for C p -analytic dynamical systems at neutral fixed points (or cycles) can be obtained from a small denominator, which is used in the construction of a congugate map for a dynamical system f having the derivative x = f '(a ) in the fixed point a.
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The Minkowski question mark function: explicit series for the dyadic period function and moments
TL;DR: In this paper, the dyadic period function G(z) was defined as a Stieltjes transform, and it was shown that the generating function of moments of F(x) satisfies the three term functional equation.
The Australian Journal of Mathematical Analysis and Applications
TL;DR: In this paper, a fixed point method for proving the Hyers-Ulam stability of the functional equation f(x + y) = f (x)f(y) f( x + y + f(y)) f(X + y)+ f(Y)+f(Y).
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Behavior of lacunary series at the natural boundary
Ovidiu Costin,M. Huang +1 more
TL;DR: In this paper, a local theory of Lacunary Dirichlet series of the form ∑ k = 1 ∞ c k exp ( − z g (k ) ), Re ( z ) > 0 as z approaches the boundary i R, under the assumption g ′ → ∞ and further assumptions on c k.