The center foliation of an affine diffeomorphism (Q1801636)

For any diffeomorphism \(f\) of a compact manifold \(M\), the center foliation \({\mathcal N}\) is defined (whenever it exists) by the distribution of all the vectors \(v\in TM\) corresponding to the Lyapunov exponent \(\lambda=0\). If \(f\) is an affine transformation of a Riemannian manifold, then \({\mathcal N}\) exists, is totally geodesic, Riemannian and transversely flat with integrable normal bundle. Several corollaries follow from this fact.