Limit Shadowing Property
Limit Shadowing Property
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DOI：
10.1080/01630569708816748
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发表时间：
1997
影响因子：
1.2
通讯作者：
T. Eirola;O. Nevanlinna;S. Pilyugin
中科院分区：
文献类型：
--
作者：
T. Eirola;O. Nevanlinna;S. Pilyugin
本文考虑离散动力系统的伪比特，使得轨道的一步误差随着指数的增加而趋于零。首先，它表明，接近双曲集，这样的轨道被遮蔽的真实轨迹的系统与遮蔽误差也趋于零。然后通过考虑伪比特使得误差序列属于某些（加权）lp-空间，并证明相应的阴影误差也存在，研究了收敛速度。在一定的权条件下，我们建立了非双曲集附近的加权跟踪。
In this paper pseudoorbits of discrete dynamical systems are considered such that the one-step errors of the orbits tend to zero with increasing indices. First it is shown that close to hyperbolic sets such orbits are shadowed by true trajectories of the system with shadowing errors also tending to zero. Then the rates of convergence are studied via considering pseudoorbits such that the error sequences belong to certain (weighted) lp-spaces and showing that the corresponding shadowing errors are there, too. Under certain conditions on the weights we establish weighted shadowing near nonhyperbolic sets.