  It is known that, for each real number x such that 1,x,x^2 are linearly
independent over Q, the uniform exponent of simultaneous approximation to
(1,x,x^2) by rational numbers is at most (sqrt{5}-1)/2 (approximately 0.618)
and that this upper bound is best possible. In this paper, we study the
analogous problem for Q-linearly independent triples (1,x,x^3), and show that,
for these, the uniform exponent of simultaneous approximation by rational
numbers is at most 2(9+sqrt{11})/35 (approximately 0.7038). We also establish
general properties of the sequence of minimal points attached to such triples
that are valid for smaller values of the exponent.
