Appendix

Abstract

Most of maps and differential equations are given explicitly in the program, but the map Q was too complicated to do this. The map Q for the study of Quasiperiodicity is defined as follows.

$$y[0] = old\_y[0] + C1 + RHO*p1/twopi\bmod 1;$$

where the functions p1 and p2 involve the lowest order sin() terms:

$$y[1] = old\_y[1] + C2 + RHO*p2/twopi\bmod 1;$$

$$p1 = A[1]*\sin (twopi*(X + k[1]) + A[2]*\sin (twopi*(Y + k[2])) + A[3]*\sin (twipo*(X + Y + k[3])) + A[4]*\sin (twopi*(X - Y + k[4]))$$

$$p2 = B[1]*\sin (twopi*(X + j[1]) + B[2]*\sin (twopi*(Y + j[2])) + B[3]*\sin (twipo*(X + Y + j[3])) + B[4]*\sin (twopi*(X - Y + j[4]))$$