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Renormalization-Plots

This is a Python program that can renormalize unimodal maps. It can renormalize any one-parameter family of unimodal maps. The plan is to also extend the functions to Henon-like maps. The program is released under the GNU General Public License version 3.

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Source code

Instructions

How to use the program

Gallery

A period-three renormalizable unimodal map

The first two images shows a period-three renormalizable unimodal map. The boxes (and vertical lines that define the intervals) are the period intervals that define the self-return map.

The third image shows the levels of rescaling.

A three-time renormalizable unimodal map (period 3-2-5 type)

The map f is period-three renormalizable. The renormalization Rf is period-two renormalizable. The second renormalization R²f is period-five renormalizable. The picture shows f, Rf, R²f, and R³f at the same time and includes the topological features of the maps.

The Route of Period Doubling.

Consider a one-parameter family of unimodal maps. As the parameter increases, the attracting fixed point bifurcates into an attracting period-two orbit of period two and a repelling fixed point. Then the attracting period-two orbit bifurcates into an attracting period-four orbit and a repelling period-two orbit. This procedure repeats as the parameter increases. The video file