Geodesic
A survey of results on density modulo $1$ of double sequences containing algebraic numbers
Communications in Mathematics, Tome 16 (2008) no. 1, pp. 31-43.

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In this survey article we start from the famous Furstenberg theorem on non-lacunary semigroups of integers, and next we present its generalizations and some related results.
Classification : 11-02, 11J71, 37A45, 54H15, 54H20
Keywords: Algebraic numbers; density modulo $1$; uniformly distributed sequences; topological dynamics; semigroups of endomorphisms; ID-semigroup; invariant sets; $a$-adic solenoids 
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Urban, Roman. A survey of results on density modulo $1$ of double sequences containing algebraic numbers. Communications in Mathematics, Tome 16 (2008) no. 1, pp. 31-43. http://geodesic.mathdoc.fr/item/COMIM_2008__16_1_a3/