Dynamical properties of linear and projective transformations and their applications (Q2487164)

The paper deals mainly with linear automorphisms of finite-dimensional vector spaces over the reals, and with the maps they induce on the corresponding projective spaces. To quote from the paper's abstract: ``We describe their dynamical properties, and their applications to certain topics in Lie groups and ergodic theory; Borel's density theorem, Halmos's question on existence of ergodic automorphisms, invariant measures of automorphisms of locally compact groups etc. This is primarily an expository article, but some new points have been brought out, corrections \(\ldots\) are noted, and some questions are raised. While for the most part we shall consider only real vector spaces, and their analogues over complex numbers, in \S 7 we shall briefly describe also analogues of the results in the case of vector spaces over \(p\)-adic fields.'' The dynamical properties described include identifying alpha and omega limit sets, the nonwandering set, and a somewhat larger set that the author calls the core of the dynamical system. This set is also sometimes referred to as the prolongational limit set.