On Dihedral Galois Coverings Arising from Lissajous’s Curves

Abstract.

We study dihedral Galois coverings arising from Lissajous’s curves by using Galois points. For any Lissajous’s curves, we can obtain dihedral Galois coverings. Indeed, if a Lissajous’s curve is closed, we find two Galois points such that its Galois group is isomorphic to the dihedral group. On the contrary, if a Lissajous’s curve is open, by taking a suitable double covering, we obtain the dihedral Galois covering. In particular, we can prove that the double covering is obtained as a space Lissajous’s curve.