Mathematica Files for the article "Birkhoff Normal Form and Twist coefficients of periodic orbits of billiards" by Xin Jin and Pengfei Zhang.



The following codes are also available at Notebook Archive


  1. The code for the one-step map of symmetric billiard table.
    twistSym.nb. See also link for a pdf copy.

  2. The code for the twice-iterated map of asymmetric billiard table.
    twistAsym.nb. See also link for a pdf copy.

    twistAsymImprove.nb (An improved version in which some intermediate expressions have been used). See also link for a pdf copy.

  3. The code for determining the coefficients of the polynomials appeared in the formula for the second twist coefficient.
    polyNQPST.nb. See also link for a pdf copy.