In:
Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), Vol. 21, No. 1 ( 2001-02), p. 303-314
Abstract:
We prove the following property: if X in \mathcal G^1(M) has no singularity and x \in \Sigma(X) , then \overline{\operatorname{orbit}(x)} \cap \overline{\operatorname{per}(X)} \not = \emptyset . In addition, if we assume \overline{\operatorname{per}_i(X)} \cap \overline{\operatorname{per}_j(X)} = \emptyset for i \not = j , then \overline{\operatorname{per}(X)} = \bigcup_{i=0}^{n-1} \overline{\operatorname{per}_i(X)} is a hyperbolic set. Moreover, we shall give a proof of the \Omega -stability conjecture for flows.
Type of Medium:
Online Resource
ISSN:
0143-3857
,
1469-4417
DOI:
10.1017/S0143385701001158
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2001
detail.hit.zdb_id:
1461798-5
SSG:
17,1
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