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 
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/
@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},
     year = {2007},
     volume = {258},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a1/}
}
TY  - JOUR
AU  - V. I. Arnol'd
TI  - Topological Classification of Trigonometric Polynomials Related to the Affine Coxeter Group $\widetilde A_2$
JO  - Informatics and Automation
PY  - 2007
SP  - 7
EP  - 16
VL  - 258
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a1/
LA  - ru
ID  - TRSPY_2007_258_a1
ER  - 
%0 Journal Article
%A V. I. Arnol'd
%T Topological Classification of Trigonometric Polynomials Related to the Affine Coxeter Group $\widetilde A_2$
%J Informatics and Automation
%D 2007
%P 7-16
%V 258
%U http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a1/
%G ru
%F TRSPY_2007_258_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Arnold V.I., “Smooth functions statistics”, Funct. Anal. and Other Mathematics, 1:2 (2006), 125–133 | MR

[2] Arnold V.I., “Statistika i klassifikatsiya topologii periodicheskikh funktsii i trigonometricheskikh mnogochlenov”, Tr. In-ta matematiki i mekhaniki UrO RAN, 12, no. 1, 2006, 15–24 | MR | Zbl

[3] Arnold V.I., Eksperimentalnoe otkrytie matematicheskikh faktov, Tsikl lektsii, prochitannykh v letnei shkole “Sovremennaya matematika” (Dubna, iyul 2005 g.), MTsNMO, M., 2006

[4] Arnold V.I., Smooth functions statistics, http://www.institut.math.jussieu.fr/seminaires/singularites/functions.pdf

[5] Arnold V.I., Smooth functions statistics, Preprint IC/2006/012, Abdus Salam Intern. Centre Theor. Phys., Trieste, 2006, 9 pp.; http://www.ictp.it/~pub\textunderscore off/ preprints-sources/2006/IC2006012P.pdf