Given a continuous fibered dynamical system, we first introduce the notion of polynomial torsion of a fiber, which measures the “infinitesimal variation” of the dynamics between the fiber and the neighboring ones. This gives rise to an (upper semicontinous) torsion function, defined on the base of the system, which is a new \(C^{0}\) (fiber) conjugacy invariant. We prove that the polynomial entropy of the system is the supremum of the torsion of its fibers, which yields a new insight into the creation of polynomial entropy in fibered systems. We examine the relevance of these results in the context of integrable Hamiltonian systems or diffeomorphisms, with the particular cases of \(C^{0}\)-integrable twist maps on the annulus and geodesic flows. Finally, we bound from below the polynomial entropy of \(\ell\)-modal interval maps in terms of their lap number and answer a question by Gomes and Carneiro.

给定连续纤维动力学系统，我们首先引入纤维多项式扭转的概念，它测量纤维与相邻纤维之间动力学的“无穷小变化”。这产生了一个（上半连续）扭转函数，在系统的基础上定义，它是一个新的 \(C^{0}\)（纤维）共轭不变量。我们证明了系统的多项式熵是其纤维扭转的上界，这为纤维系统中多项式熵的创建提供了新的见解。我们在可积哈密顿系统或微分同胚的背景下检查这些结果的相关性，以及环空和测地流上\(C^{0}\) -可积扭曲图的特殊情况。最后，我们从下面将\(\ell\)模态区间图的多项式熵与圈数联系起来，并回答 Gomes 和 Carneiro 的问题。