In this paper we give the complete description of the structure of compact global (forward) attractors for non-autonomous perturbations of autonomous gradient-like dynamical systems under the assumption that the original autonomous system has a finite number of hyperbolic stationary solutions. We prove that the perturbed non-autonomous (in particular \(\tau \)-periodic, quasi-periodic, Bohr almost periodic, almost automorphic, recurrent in the sense of Birkhoff) system has exactly the same number of invariant sections (in particular the perturbed systems has the same number of \(\tau \)-periodic, quasi-periodic, Bohr almost periodic, almost automorphic, recurrent in the sense of Birkhoff solutions). It is shown the compact global (forward) attractor of non-autonomous perturbed system coincides with the union of unstable manifolds of this finite number of invariant sections.

中文翻译：

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梯度动力系统非自治摄动的全局吸引子的结构

在本文中，我们在假设原始自治系统具有有限数量的双曲平稳解的假设下，完整描述了紧凑的全局（正向）吸引子的结构，这些结构用于自治梯度式动力学系统的非自治扰动。我们证明扰动的非自治（特别是\（\ tau \） -周期，拟周期，玻尔（在Birkhoff的意义上几乎是周期性的，几乎是自胚的，递归的）周期）具有完全相同数量的不变部分（特别是扰动的系统具有相同的\（\ tau \）周期，准周期，玻尔（在Birkhoff解的意义上几乎是周期性的，几乎是同构的）递归的）。结果表明，非自治扰动系统的紧凑全局（前向）吸引子与该有限数目的不变截面的不稳定歧管的并集相吻合。