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- W2024195467 abstract "For a given meromorphic function $g:mathbb Cto mathbb C$, we study the locus of points $z$ that are {it collinear} with their two iterations $g(z)$ and $g(g(z))$. Such points form a {it collinearity curve}. Generally, this curve is reducible: it has several components. Components of the curve, especially algebraic ones, are investigated. The curve{'}s behavior near a fixed point of the function is explored. We also look into the asymptotic structure of the curve at infinity. The components of the curve are interpretable as vertices and edges of a graph resembling a Voronoi diagram. The collinearity curve, needing a mere two iterates, may help us in understanding the long-term dynamics of the original function on $mathbb C$ and in visualizing important features of the generated fractal for $g$ and its associated Voronoi diagram." @default.
- W2024195467 created "2016-06-24" @default.
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- W2024195467 date "2012-06-01" @default.
- W2024195467 modified "2023-09-25" @default.
- W2024195467 title "Collinearity of Iterations and Real Plane Algebraic Curves" @default.
- W2024195467 cites W1967005434 @default.
- W2024195467 doi "https://doi.org/10.1109/isvd.2012.23" @default.
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