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2012 Plotting basins of end points of rational maps with Sage
Luis Javier Hernández Paricio, Miguel Marañón Grandes, María Teresa Rivas Rodríguez
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Tbilisi Math. J. 5(2): 71-99 (2012). DOI: 10.32513/tbilisi/1528768904

Abstract

The aim of this work is to present a new program written in Sage which allows us to visualize the attraction basins associated to the end points of a discrete semi-flow induced by a rational function on the Riemann sphere by using its geometry and complex structure. One interesting novelty brought by the developed program is that it is able to plot fractals not only in a determined rectangular area of the complex plane, but also on the whole surface of the Riemann sphere. Another advantage of the program is that it permits us to visualize not only the attraction basins of fixed points, but also the basins of end points associated with periodic points. In addition, some applications of the described algorithms to Numerical Analysis and Fractal Geometry are suggested.

Acknowledgment

The authors acknowledge the financial help given by project API12/10.

Citation

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Luis Javier Hernández Paricio. Miguel Marañón Grandes. María Teresa Rivas Rodríguez. "Plotting basins of end points of rational maps with Sage." Tbilisi Math. J. 5 (2) 71 - 99, 2012. https://doi.org/10.32513/tbilisi/1528768904

Information

Published: 2012
First available in Project Euclid: 12 June 2018

zbMATH: 1280.37001
Digital Object Identifier: 10.32513/tbilisi/1528768904

Subjects:
Primary: 37-04
Secondary: 00A66, 14E05

Rights: Copyright © 2012 Tbilisi Centre for Mathematical Sciences

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Vol.5 • No. 2 • 2012
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