AI 中文总结
该研究构造具有无限拓扑熵的同胚稠密集合，其伪奇异悬浮流有有限熵，证明同胚剩余集的伪奇异悬浮流保持正熵，还证对于\(n \geq 2\)的紧致\(n\)维流形存在相关极小同胚及零熵伪奇异悬浮流，揭示熵无限性在奇异重参数化下的脆弱性。
AI 中文摘要
我们构造了一个具有无限拓扑熵的同胚稠密集合，其相关的伪奇异悬浮流具有有限熵，甚至可以达到任意小的正值，这表明无限熵在奇异时间变化下不被保留。作为补充，我们证明对于同胚的一个剩余集，所有伪奇异悬浮流都保持正熵。我们还证明对于任何\(n \geq 2\)，存在一个紧致\(n\)维流形，它允许一个具有无限拓扑熵的极小同胚；对于这样的极小同胚，一个适当选择的具有单个奇点的伪奇异悬浮流具有零熵。我们的结果表明，虽然熵的正值通常是稳定的，但在奇异重参数化下其无限性是脆弱的。
英文摘要
We construct a dense set of homeomorphisms with infinite topological entropy whose associated pseudo-singular suspension flows have finite entropy -- and indeed, arbitrarily small positive values can be achieved -- showing that infinite entropy is not preserved under singular time changes. Complementing this, we prove that for a residual set of homeomorphisms, all pseudo-singular suspensions retain positive entropy. We also prove that for any $n \geq 2$, there exists a compact n-dimensional manifold admitting a minimal homeomorphism with infinite topological entropy; for such minimal homeomorphisms, a suitably chosen pseudo-singular suspension with a single singularity has zero entropy. Our results reveal that while positivity of entropy is generically stable, its infinitude is fragile under singular reparametrizations.
Comments18 pages, 1 figure
