Geodesic
Topological Classification of Trigonometric Polynomials Related to the Affine Coxeter Group~$\widetilde A_2$
Informatics and Automation, Analysis and singularities. Part 1, Tome 258 (2007), pp. 7-16

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Trigonometric polynomials on the 2-torus that belong to a special six-parameter family are classified up to diffeomorphisms of the image and the preimage that are homotopic to the identity. 
@article{TRSPY_2007_258_a1,
     author = {V. I. Arnol'd},
     title = {Topological {Classification} of {Trigonometric} {Polynomials} {Related} to the {Affine} {Coxeter} {Group~}$\widetilde A_2$},
     journal = {Informatics and Automation},
     pages = {7--16},
     publisher = {mathdoc},
     volume = {258},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a1/}
}
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V. I. Arnol'd. Topological Classification of Trigonometric Polynomials Related to the Affine Coxeter Group~$\widetilde A_2$. Informatics and Automation, Analysis and singularities. Part 1, Tome 258 (2007), pp. 7-16. http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a1/