A recurrence property of smooth functions Academic Article uri icon

abstract

  • LetP andQ be real polynomials of degreesd ande, respectively, andf a periodic function. It is shown that, iff iss times differentiable atQ(0), wheres≧7de 3 log 14e 3, then for every ɛ>0 the diophantine inequality ≧FF5C;P(x)f(Q(x)) -P(0)f(Q(0)) -y≧ εx≠0, has a solution. This settles in particular a question raised by Furstenberg and Weiss [6].

publication date

  • January 1, 1988