逐点伪轨跟踪性质及其应用(英文)

Pointwise Pseudo-Orbit Tracing Property and Its Application

中文关键词:  敏感依赖  伪轨跟踪性质

英文关键词:sensitive dependence  pseudo-orbit tracing property

中文摘要:

      本文给出紧致度量空间逐点伪轨跟踪性质的定义,该定义是伪轨跟踪性质定义的推广.作为应用,证明如下结论:(i)若f具有逐点伪轨跟踪性质,且对任意k∈Z₊, f^k为链转换的,那么对任意k∈Z₊, f^k为开集转换;(ii)若f具有逐点伪轨跟踪性质,且对任意n∈Z₊, fⁿ为链转换的,则f具有初始敏感依赖性质;(iii)若f为开集混合的,且具有逐点伪轨跟踪性质,那么f具有性质P;(iv)设f:(X,d)→(X,d)是同胚映射,那么f具有逐点伪轨跟踪性质当且仅当移位映射σ_f具有逐点伪轨跟踪性质.

英文摘要:

      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 f has pointwise pseudo-orbit tracing property, for any k ∈ Z₊, and f^k is chain transitive, then for any k ∈ Z₊, f^k 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 haspointwise 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 σ_f is pointwise pseudo-orbit tracing property.