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Univalent functions and the Schwarzian derivative
Commentarii Mathematici Helvetici, 1977 openaire +2 more sources
The Schwarzian derivative and the Poincaré metric [PDF]
Pacific Journal of Mathematics, 1979 openaire +3 more sources
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Pre-Schwarzian and Schwarzian derivatives of logharmonic mappings
Monatshefte für Mathematik, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V. Bravo +3 more
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2020
The Schwarzian derivative of a function f is a rational function of the derivatives of f to order 3. In fact it can be expressed in terms of the logarithmic derivative \(f''/f'\) of \(f'\). Here we show that the Schwarzian derivative is a natural object: a measure of the “curvature” of f, the pointwise deviation from a best approximation of f by a ...
Richard Beals, Roderick S. C. Wong
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The Schwarzian derivative of a function f is a rational function of the derivatives of f to order 3. In fact it can be expressed in terms of the logarithmic derivative \(f''/f'\) of \(f'\). Here we show that the Schwarzian derivative is a natural object: a measure of the “curvature” of f, the pointwise deviation from a best approximation of f by a ...
Richard Beals, Roderick S. C. Wong
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Schwarzian derivative in Kähler manifolds (II)
Science in China Series A: Mathematics, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gong, Sheng, Yu, Qihuang, Na, Jisheng
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Negative Schwarzian Derivative
2009We now ask how many stable periodic orbits a unimodal map can have. This question was first asked by Julia, in 1918. How showed that for certain unimodal maps which are restrictions to [-1,1] of analytic functions, there can be at most one stable periodic orbit. In particular, his theory applies to f(x) = 1 − μx2, 0 < μ ≤ 2. But a real breakthrough has
Pierre Collet, Jean-Pierre Eckmann
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Schwarzian derivative and convexity of order $$\alpha$$
The Journal of Analysis, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Somya Malik, V. Ravichandran
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On Iterated Positive Schwarzian Derivative Maps
International Journal of Bifurcation and Chaos, 2003We study the behavior of a unimodal map in two parameters, one of the parameters varies the sign of the Schwarzian derivative the second the value of the maximum. We characterize the behavior of the different dynamics in the parameter space.
Oliveira, Henrique, Sousa Ramos, J.
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1987
In this chapter we define, as a generalization of the Schwarzian derivative introduced in Chapter 4, a system of PGL (n+1, ℂ)-invariant operators S ij k . (1 ≦ i, j, k ≦ n) on non-degenerate maps of n-variables, where we assume n ≧ 2. These operators will be key tools for constructing uniformizing equations in Chapters 10 and 12.
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In this chapter we define, as a generalization of the Schwarzian derivative introduced in Chapter 4, a system of PGL (n+1, ℂ)-invariant operators S ij k . (1 ≦ i, j, k ≦ n) on non-degenerate maps of n-variables, where we assume n ≧ 2. These operators will be key tools for constructing uniformizing equations in Chapters 10 and 12.
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