Daniel Berend

Furstenberg's theorem asserts that the double sequence is dense modulo one for every irrational. The same holds with and replaced by any two multiplicatively independent integers. Here we obtain the same result for the sequences for any non-negative integer and irrational, and for the sequence, where is any polynomial with at least one irrational coefficient. Similarly to Furstenberg's theorem, both results are obtained by considering appropriate dynamical systems.