We exhibit self-similar sets on the line which are not exponentially separated and do not generate any exact overlaps. Our result shows that the exponential separation, introduced by Hochman in his groundbreaking theorem on the dimension of self-similar sets, is too weak to describe the full theory.

中文翻译：

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超指数冷凝，无精确重叠

我们在线上展示自相似集，它们没有按指数分隔，并且不会产生任何确切的重叠。我们的结果表明，霍赫曼（Hochman）在他的开创性定理中关于自相似集的维数引入的指数分离太弱，无法描述完整的理论。