Skew products and nonremovable Lyapunov exponents.
Abstract. Recently Gorodetski, Kleptsyn, Nalski and the speaker found an open set in the space of dynamical systems on a three-torus, for any map of which there exists a nonhyperbolic nonatomic ergodic invariant measure. Nonhyperbolicity means that the measure has an (intermediate) zero Lyapunov exponent. This result is a part of a large program suggested by Gorodetski and Ilyashenko in 1998.