论文标题
在Banach空间上部分双曲动力学的准阴影
Quasi-shadowing for partially hyperbolic dynamics on Banach spaces
论文作者
论文摘要
据说，如果每个伪造的属性都可以通过点$（x_n）_ {n \ in \ z} $来遮蔽，则可以将部分双曲动力学系统具有准遮盖属性。在本文中，我们证明了作用于任意Banach空间的线性算子（不一定是可逆的）线性算子的部分二分法序列的小非线性扰动具有准阴影特性。我们还获得了此结果的连续时间版本。作为我们主要结果的应用，我们证明了线性运算符的某些部分部分二分法序列稳定在中心方向上的运动。
A partially hyperbolic dynamical system is said to have the quasi-shadowing property if every pseudotrajectory can be shadowed by a sequence of points $(x_n)_{n\in \Z}$ such that $x_{n+1}$ is obtained from the image of $x_n$ by moving it by a small factor in the central direction. In the present paper, we prove that a small nonlinear perturbation of a partially dichotomic sequence of (not necessarily invertible) linear operators acting on an arbitrary Banach space has the quasi-shadowing property. We also get obtain a continuous time version of this result. As an application of our main result, we prove that a certain class of partially dichotomic sequences of linear operators is stable up to the movement in the central direction.
