In this paper, the pointwise pseudo-orbit tracing property is defined on a compact metric space, and it is a generalization of pseudo-orbit tracing property. As applications, we prove the following results: (i) If / h...In this paper, the pointwise pseudo-orbit tracing property is defined on a compact metric space, and it is a generalization of pseudo-orbit tracing property. As applications, we prove the following results: (i) If / has pointwise pseudo-orbit tracing property, for any k ∈ Z+, and fk is chain transitive, then for any k ∈ Z+, fk has open set transitive ; (ii) If f has pointwise pseudo-orbit tracing property, and for any n ∈ Z+,fn is chain transitive, then f has sensitive dependence on initial conditions; (iii) If f is open set mixing and has pointwise pseudo-orbit tracing property, then f has property P; (iv) Let f : (X, d) →(X, d) be a homeomophism, then f is pointwise pseudo-orbit tracing property if and only if the shift map σf is pointwise pseudo-orbit tracing property.展开更多
文摘In this paper, the pointwise pseudo-orbit tracing property is defined on a compact metric space, and it is a generalization of pseudo-orbit tracing property. As applications, we prove the following results: (i) If / has pointwise pseudo-orbit tracing property, for any k ∈ Z+, and fk is chain transitive, then for any k ∈ Z+, fk has open set transitive ; (ii) If f has pointwise pseudo-orbit tracing property, and for any n ∈ Z+,fn is chain transitive, then f has sensitive dependence on initial conditions; (iii) If f is open set mixing and has pointwise pseudo-orbit tracing property, then f has property P; (iv) Let f : (X, d) →(X, d) be a homeomophism, then f is pointwise pseudo-orbit tracing property if and only if the shift map σf is pointwise pseudo-orbit tracing property.
