Embedding lattice actions in flows with multidimensional time

The genericity of the embeddability of lattice actions in flows with multidimensional time is studied. In particular, questions of de la Rue and de Sam Lazaro on the genericity of the embeddability of an action of a 2-lattice in a flow and the embeddability of a transformation in injective flow actions with multidimensional time are answered. It is also shown that a generic transformation has a set of roots of continuum cardinality in an arbitrary prescribed massive set.