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No-shadowing for singular hyperbolic sets with a singularity
Discrete and Continuous Dynamical Systems ( IF 1.1 ) Pub Date : 2020-06-29 , DOI: 10.3934/dcds.2020258 Xiao Wen , , Lan Wen ,
Discrete and Continuous Dynamical Systems ( IF 1.1 ) Pub Date : 2020-06-29 , DOI: 10.3934/dcds.2020258 Xiao Wen , , Lan Wen ,
We prove that every singular hyperbolic chain transitive set with a singularity does not admit the shadowing property. Using this result we show that if a star flow has the shadowing property on its chain recurrent set then it satisfies Axiom A and the no-cycle conditions; and that if a multisingular hyperbolic set has the shadowing property then it is hyperbolic.
中文翻译:
具有奇异性的双曲奇异集的无阴影
我们证明具有奇异性的每个奇异双曲链传递集都不允许遮蔽性。利用这个结果,我们表明,如果一个恒星流在其链的递归集合上具有遮蔽特性,则它满足公理A和无循环条件;并且,如果多奇双曲集具有阴影属性,则它是双曲的。
更新日期:2020-07-20
中文翻译:
具有奇异性的双曲奇异集的无阴影
我们证明具有奇异性的每个奇异双曲链传递集都不允许遮蔽性。利用这个结果,我们表明,如果一个恒星流在其链的递归集合上具有遮蔽特性,则它满足公理A和无循环条件;并且,如果多奇双曲集具有阴影属性,则它是双曲的。