Viorel Nitica (West Chester University)

Transitivity of euclidean extensions of Anosov diffeomorphisms.

Abstract. Let X be an infranilmanifold, $T:X\to X$ an Anosov diffeomorphism, $f:X\to{\mathbb R}^n$ a Holder function, and T_f the skew-product determined by T and f. Then the following are equivalent:

1)

T_f is topologically transitive;

2)

T_f is stably topologically transitive;

3)

T_f has orbits with projections arbitrarily large in any direction;

4)

T_f satisfies the following Inseparability Hypothesis: the weights of T_f over the periodic points are separated by any hyperplane.