科研之友
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摘要
In this paper, we prove a generalized shadowing lemma. Let f is an element of Diff(M) Assume that A is a closed invariant set of f and there is a continuous invariant splitting TLambdaM = E + F on Lambda. For any lambda is an element of (0, 1) there exist L > 0, d(o) > 0 such that for any d is an element of (0,d(o)] and any lambda-quasi-hyperbolic d-pseudoorbit {x(i), n(i)}(i=-infinity)(infinity), there exists a point x which Ld-shadows {x(i), n(i)}(i=-infinity)(infinity). Moreover, if {x(i), n(i)}(i=-infinity)(infinity), is periodic, i.e., there exists an m > 0 such that x(i)+m = x(i) and n(i)+m = n(i) for all i, then the point x can be chosen to be periodic.
- 出版日期2002-7
- 单位北京大学
