We show that the Szekeres system with cosmological constant admits a sufficient number of conservation laws, which allow to claim the integrability of the system. The main novelty in this investigation is that we find that the unique attractor of the Szekeres system is the isotropic inhomogeneous de Sitter (-like) Universe, contrary to the original system in which the attractors describe Kantowski–Sachs (-like) spacetimes. We also study the existence of quantum corrections and the emergence of classicality by considering the linear and quadratic conserved quantities at the quantum level. We perform an analysis considering different approaches, involving the Bohmian quantum potential and a probability analysis. The result is that there are no quantum corrections for the quadratic integrals, while there exists a linear case for which we find quantum corrections.

我们表明具有宇宙常数的 Szekeres 系统承认足够数量的守恒定律，这允许声称系统的可积性。这项研究的主要新颖之处在于，我们发现 Szekeres 系统的独特吸引子是各向同性非均匀 de Sitter（类）宇宙，这与吸引子描述 Kantowski-Sachs（类）时空的原始系统相反。我们还通过考虑量子级别的线性和二次守恒量来研究量子修正的存在和经典性的出现。我们考虑不同的方法进行分析，包括玻姆量子势和概率分析。结果是二次积分没有量子修正，