| 李明军.逐点伪轨跟踪性质及其应用(英文)[J].数学研究及应用,2005,25(1):23~30 |
| 逐点伪轨跟踪性质及其应用(英文) |
| Pointwise Pseudo-Orbit Tracing Property and Its Application |
| 投稿时间：2002-11-27 |
| DOI：10.3770/j.issn:1000-341X.2005.01.003 |
| 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 |
| 基金项目: |
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| 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+, fk为链转换的,那么对任意k∈Z+, fk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σf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 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 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 σf is pointwise pseudo-orbit tracing property. |
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