Remarks on isorigidity, centralizers, and spectral equivalence in ergodic theory (Q2460541)

Let \(R\) be a binary relation acting on invertible transformations \(T:M\to M\) preserving a given probabilistic measure on the manifold \(M\). The authors introduce the invariant \(f_R(T)\) defined as the maximum cardinality of families \(\{T_\alpha\}\) of pairwise nonisomorphic maps such that the relation \(R\) holds for any pair \((T,T_\alpha)\). They describe maximum values of the invariant \(f_R(T)\) and study its generic values.