Kolmogorov-Sinai entropy for \(p\)-preserving systems
The paper develops a theory of entropy in the realm of a \(gs\)-space \((L,p)\) involving the notion of a generalized \(s\)-map. By a generalized \(s\)-map on a lattice \(L\), the authors mean a monotonic mapping \(p:L\times L\to[0,1]\) satisfying \(p(1,1)=1\). The authors study the dynamics of a \(p\)-preserving system \((L,p,\phi)\). They say that the entropy of \(p\)-preserving systems is isomorphism invariant and the entropy of an invertible \(p\)-preserving system vanishes provided the corresponding Rokhlin space admits a one-sided generator.
scientific article; zbMATH DE number 6824705