The goal of the project is to find pre-periodic points of a dynamical system defined over function fields by implementing the Hutz algorithm in the open-source environment Sage based on the Python language, using algebraic and arithmetic properties of the function field to calculate the pre-periodic points more efficiently.
By using the algorithm we want to get a list of graphs of periodic points similar to the Poonen conjecture.
In the test folder, there's Jupyter Notebook file which has some python code to test the functions we added to Sage, we put the functions we wrote at the start of the file and after that, we ran these functions on some dynamic systems we chose to show the graphs of the pre-periodic points.
In the images folder, there are some pictures of the graphs we got after running the algorithm on many Dynamic Systems defined over Function Fields over Finite Field .
Graph of pre-periodic points :
are periodic points (also pre-periodic).
are only pre-periodic points because after several iterations they become periodic (as shown in the picture above)
➡️Input:
- A dynamical system defined over 𝑭𝒒(𝒕) (function fields) where 𝑭 is a finite field .
⬅️Output:
- Graph of all the pre-periodic points of the dynamical system.