发表机构
Faculty of Mathematics, University of Rijeka; Department of Mathematics, University of Pannonia（里耶卡大学数学系; 佩奇大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出广义伪双曲性概念，证明其对巴拿赫空间上可逆有界线性算子序列等价于阴影性与拓扑稳定性，并在自治情形下简化了等价条件，同时证明了稳健性。
AI 中文摘要
尽管广义双曲性已被证明是线性动力学中的一个基本概念，但最近的结果表明，它在刻画巴拿赫空间上可逆有界线性算子的阴影性方面过于严格。这促使我们引入广义伪双曲性，这是一种通过生成指数衰减格林族的连续齐次映射来表述的更弱的概念。我们证明，对于巴拿赫空间上任意可逆有界线性算子序列，广义伪双曲性等价于阴影性和拓扑稳定性。在自治情形下，这得到了阴影性与拓扑稳定性之间的等价性，去除了先前结果中的额外假设。我们还证明了可逆有界线性算子序列的阴影性和拓扑稳定性的稳健性。
英文摘要
Although generalized hyperbolicity has proved to be a fundamental notion in linear dynamics, recent results show that it is too restrictive to characterize the shadowing property of invertible bounded linear operators on Banach spaces. This motivates the introduction of generalized pseudo-hyperbolicity, a weaker notion formulated through continuous homogeneous maps generating exponentially decaying Green families. We prove that, for arbitrary sequences of invertible bounded linear operators on Banach spaces, generalized pseudo-hyperbolicity is equivalent to both shadowing and topological stability. In the autonomous setting, this yields the equivalence between shadowing and topological stability, removing additional assumptions from previous results. We also prove robustness of shadowing and topological stability for sequences of invertible bounded linear operators.
