The generalized Chazy equation and Schwarzian triangle functions
نویسندگان
چکیده
منابع مشابه
Symmetry and the Chazy Equation
There are three di erent actions of the unimodular Lie group SL on a two dimensional space In every case we show how an ordinary di erential equation admitting SL as a symmetry group can be reduced in order by three and the solution recovered from that of the reduced equation via a pair of quadratures and the solution to a linear second order equation A particular example is the Chazy equation ...
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The Chazy equation y′′′ = 2yy′′ − 3y′2 is derived from the automorphic properties of Schwarz triangle functions S(α, β, γ; z). It is shown that solutions y which are analytic in the fundamental domain of these triangle functions, only correspond to certain values of α, β, γ. The solutions are then systematically constructed. These analytic solutions provide all known and one new parametrization...
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For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$, we definea subclass of the spirallike functions, $SP_{p}(alpha)$, the setof all functions $fin mathcal{A}$[releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative $mathrm{T}...
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It is customary to formulate the inequalities of the "Verzerrungssatz" type for analytic functions w—f(z), schlicht in the unit circle, with reference to a specific normalization. The two normalizations mainly used are: (a) f(z) is finite in \z\ < 1 , /(O) = 0 , /'(O) = 1; (b) ƒ(z) has a pole at 2 = 0 with the residue 1. If we want to obtain inequalities which are independent of any particular ...
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ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 1998
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.1998.v2.n4.a1