标题： 广义抛物线动力系统的熵 显示英文标题

标题： Entropy for Generalized Parabolic Dynamics

摘要： 在本文中，我们将广义熵的概念扩展到一致空间，使得在可度量化的设定之外也能进行计算。 我们将其应用于抛物动力系统——在两个时间方向上统一吸引所有紧致子集的具有唯一不动点的系统，并引入一个更广泛的类，称为广义抛物动力系统。 在其中，我们识别出一个重要子类，并证明其线性熵，提供了几种等价刻画，将空间的广义熵、非游荡集以及相互奇异子集族联系起来。 我们还研究了具有单元素非游荡集但非抛物动力系统的紧致曲面同胚。 我们提出的例子至少具有二次熵，在多项式增长速率的上界内。 对于这些界限内具有线性不变性质的任何增长速率，我们构造了一个广义熵实现预定增长的同胚，且非游荡集被简化为一点。 显示英文摘要

摘要： In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact subsets in both time directions - and introduce a broader class, called generalized parabolic dynamics. Within this, we identify a significant subclass and prove its linear entropy, offering several equivalent characterizations linking the generalized entropy of the space, the non-wandering set, and families of mutually singular subsets. We also study homeomorphisms of compact surfaces with a singleton non-wandering set but non-parabolic dynamics. The examples that we present have at least quadratic entropy, bounded above by the supremum of polynomial growth rates. For any growth rate with the linear invariant property within these bounds, we construct a homeomorphism whose generalized entropy realizes the prescribed growth, with the non-wandering set reduced to a point.