Our knowledge on Chaos theory is practically zero. Can anyone help us figuring out and explaining pattern of the chaos (please check out the figures only)
Preprint Chaos Theory Approximation
We have not found any research paper or textbook referring to this recurrence. Can you help us to explain these problems in terms of chaos theory?
You could calculate a the Lyapunov exponent of this map. Here are some lecture notes I found on how to do this: https://courses.physics.ucsd.edu/2017/Spring/physics221a/Phys_221A_Lecture_4-5.pdf You could also try to see the behavior of the series as the number of iterations tends to infinity for both real and complex numbers. Here is an example of this map in real space. The Y axis is x_n from 0 to 5. Note pattern of triangular shapes decaying quickly into chaos.
If you have time, I think following lectures could be useful for you
https://www.youtube.com/watch?v=FZu87ME2Ekk&list=PLVbyDf9daF9tFUpKqKzkzfEg-mRooTVAs&index=21
https://www.youtube.com/watch?v=wxQaTCkbkV8&list=PLVbyDf9daF9tFUpKqKzkzfEg-mRooTVAs&index=22
https://www.youtube.com/watch?v=Z1x-HofEV7A&list=PLVbyDf9daF9tFUpKqKzkzfEg-mRooTVAs&index=23
https://www.youtube.com/watch?v=YVtUTL_UzA0&list=PLVbyDf9daF9tFUpKqKzkzfEg-mRooTVAs&index=24
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