扩张迭代函数系的相对变分原理
A Relative Variational Principle for Expanding Iterated Function Systems
AI总结：
本文针对一类扩张迭代函数系，证明了相对变分原理，利用非平稳Ruelle-Perron-Frobenius定理建立了符号基遍历不变测度下边缘熵与诱导斜积纤维平均拓扑熵的关系。
AI中文摘要：
变分原理是研究混沌动力系统不变测度的关键工具。近年来，动力学家在随机和非平稳系统中开发了技术以更好地建模现实世界现象。在此，我们证明了一类扩张迭代函数系的相对变分原理。特别地，我们使用非平稳Ruelle-Perron-Frobenius定理证明，在符号基上的遍历不变测度下的边缘熵等于诱导斜积中沿纤维的平均拓扑熵。
英文摘要：
The variational principle is a key tool in the study of invariant measures for chaotic dynamical systems. In recent times, dynamicists have developed techniques in random and nonstationary systems to better model real-world phenomena. Here, we prove a relative variational principle for a class of expanding iterated function systems. In particular, we use a nonstationary Ruelle--Perron--Frobenius theorem to show that the marginal entropy given an ergodic invariant measure on the symbolic base equals the average topological entropy along fibers in the induced skew product.
