On the structure of sets of lattice points in the plane with a small doubling property
Structure theory of set addition, Astérisque, no. 258 (1999), pp. 217-240 
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     author = {Stanchescu, Yonutz V.},
     title = {On the structure of sets of lattice points in the plane with a small doubling property},
     booktitle = {Structure theory of set addition},
     editor = {Deshouilliers Jean-Marc and Landreau Bernard and Yudin Alexander A.},
     series = {Ast\'erisque},
     pages = {217--240},
     year = {1999},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {258},
     mrnumber = {1701200},
     zbl = {0979.11018},
     language = {en},
     url = {https://www.numdam.org/item/AST_1999__258__217_0/}
}
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Stanchescu, Yonutz V. On the structure of sets of lattice points in the plane with a small doubling property, dans Structure theory of set addition, Astérisque, no. 258 (1999), pp. 217-240. https://www.numdam.org/item/AST_1999__258__217_0/

[B] Bilu Y., Structure of sets with small sumsets, Mathématiques Stochastiques, Univ. Bordeaux 2, Preprint 94-10, 1994.

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