Group actions: Entropy, mixing, spectra, and generic properties

We talk about several directions of V. Rokhlin’s heritage in ergodic theory: ideas that influenced the further development of investigations (genericity, approximations), problems put forward by V. Rokhlin in his papers, problems that V. Rokhlin put forward verbally (in particular, the question about homogeneous spectrum of finite multiplicity). We touch upon the directions close to the authors of this text and their school. Many of the questions raised by Rokhlin have analogs for different classes of transformations, for group actions, and versions about the genericity of properties appearing in these formulations. We will consider the corresponding topics in such a generalized sense.