Real-quadratic-rational-maps

The project was motivated by the elegant paper of John Milnor on quadratic rational maps https://bit.ly/3623BqT.
This work is a part of my PhD Thesis https://bit.ly/3i11JRN.
The codes for computing topological entropy have been used in papers http://bitly.ws/AfAP and https://bit.ly/2RW8CsQ.
In the Bifurcation folder, Codes bifurcation1.m through bifurcation5.m and bifurcationlogistic.m generate bifurcation diagrams for certain 1-parameter families of real quadratic rational maps.

Codes in folders Entropy_Unimodal and Entropy_Bimodal compute the topological entropy for unimodal or bimodal interval maps in the normal form x->2.mu.x(tx+2)/((tx+2)^2+mu^2.x^2):[-1,1]->[-1,1]
The (mu,t)-parameter space of these maps can be divided into seven regions based on the modality and the shape of these interval maps. Interesting entropy behavior emerges only for families of unimodal and (+-+)-bimodal maps (see http://bitly.ws/AfAP).
The codes in the Entropy_Unimodal folder are based on the algorithm introduced in https://bit.ly/3kLnC9g.
The codes in the Entropy_Bimodal folder are based on the algorithm introduced in https://bit.ly/3kH8B8D.