Dynamical systems and transformation groups: entropy, mixing, spectra and generic properties

1.Isospectrality, homogeneous spectra of finite multiplicity, values of multiplicity function, multiplicative ergodic theorem.
2.Inclusion of transformations into flows, multiple mixing and invariants of sigma-algebras filtrations.
3.Generic properties, mappings preserving category of sets, inheriting of generic properties, approximation of group actions.