As it is well-known, the forwards and pullback dynamics are in general unrelated. In this paper we present an in-depth study of whether the pullback attractor is also a forwards attractor for the processes involved with the skew-product semiflow induced by a family of scalar non-autonomous reaction-diffusion equations which are linear in a neighbourhood of zero and have null upper Lyapunov exponent. Besides, the notion of Li-Yorke chaotic pullback attractor for a process is introduced, and we prove that this chaotic behaviour might occur for almost all the processes. When the problems are additionally sublinear, more cases of forwards attraction are found, which had not been previously considered even in the case of linear-dissipative ODEs.

中文翻译：

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标量非自治线性耗散抛物线偏微分方程中的前向吸引力属性。零上李雅普诺夫指数的情况

众所周知，前进和后退的动态通常是无关的。在本文中，我们深入研究了回拉吸引子是否也是前向吸引子，用于涉及由一系列标量非自治反应扩散方程引起的偏积半流所涉及的过程，这些方程在邻域内是线性的零且上李雅普诺夫指数为零。此外，引入了一个过程的 Li-Yorke 混沌回撤吸引子的概念，我们证明了这种混沌行为可能发生在几乎所有的过程中。当问题另外是次线性的时，会发现更多的前向吸引力案例，即使在线性耗散 ODE 的情况下也没有考虑过。