Lowering topological entropy over subsets revisited

الأصل · EN

Let (X, T) be a topological dynamical system. Denote by h (T, K) and hᵇ (T, K) the covering entropy and dimensional entropy of K X, respectively. (X, T) is called D- lowerable (resp. lowerable) if for each 0≤ h≤ h (T, X) there is a subset (resp. closed subset) Kₕ with hᵇ (T, Kₕ)= h (resp. h (T, Kₕ)= h); is called D- hereditarily lowerable (resp. hereditarily lowerable) if each Souslin subset (resp. closed subset) is D-lowerable (resp. lowerable). In this paper it is proved that each topological dynamical system is not only lowerable but also D-lowerable, and each asymptotically h-expansive system is D-hereditarily lowerable. A minimal system which is lowerable and not hereditarily lowerable is demonstrated.