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The Schwarzian derivative in several complex variables IV
Science in China Series A: Mathematics, 1998The authors consider the Schwarzian derivative of a holomorphic \(n\times n\) matrix mapping \(W\) of an \(n\times n\) matrix variable \(Z\) along the direction \(Z\) and receive a necessary and sufficient condition of the transformation of this derivative to zero. [Part I: \textit{S. Gong} and \textit{C. H. FitzGerald}, Sci. China, Ser. A 36, No.
Gong, Sheng, Yu, Qihuang, Zheng, Xuean
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Note on the Schwarzian derivative
Chaos, Solitons & Fractals, 1996Abstract The Schwarzian derivative is usually assumed to be negative throughout the complete interval of the dynamic variable in a one-dimensional dynamic system with chaotic behaviour. A case is reported where it is positive in the first few percent of this interval.
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Discretization of the Schwarzian derivative
AIP Conference Proceedings, 2016Numerical treatment of the Schwarzian derivatives from the exact discretization point is useful for many applications. Since we found the discrete counterpart of Schwarzian derivative is the Cross-ratio, we can regard the Cross-ratio to the discrete conformal mapping function instead of the Schwarzian derivative.
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About the Cover: The Schwarzian Derivative
Computational Methods and Function TheoryzbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Functions with Negative Schwarzian Derivatives
2015This chapter is devoted to the analysis on functions with NSD (negative Schwarzian derivatives). First, basic properties of functions with NSD are given and a classification result is proven for such functions. Then, an analysis is made on the fixed points for functions with NSD.
Mehmet Eren Ahsen +2 more
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Newton's method and Schwarzian derivatives
Journal of Dynamics and Differential Equations, 1994The author investigates the Newton method when it converges to a fixed point with orders of convergence greater than 2. He also shows the role of Schwarzian derivative in this convergence property.
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Halley's method and schwarzian derivatives
Applicable Analysis, 1996Halley's method is derived and compared with Newton's method. We show that Halley's method converges to a regular zero of a function of with an order of convergence that equals or exceeds 3. We prove for a quadratic irrational that Halley's method is equivalent to f3(z) which was derived previously.
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Schwarzian derivatives and uniformization
2002Takeshi Sasaki, Masaaki Yoshida
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