This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which applies to explicit problems in non-perturbative regimes. We obtain verifiable lower bounds on the regularity of the attractor in terms of the ratio of the expansion rate on the torus with the contraction rate near the torus. We consider separately two important cases of rotational and resonant tori. In the rotational case we obtain $ C^k $ lower bounds on the regularity of the embedding. In the resonant case we verify the existence of tori which are only $ C^0 $ and neither star-shaped nor Lipschitz.

中文翻译：

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ODE的二维吸引不变圆托的计算机辅助证明

这项工作研究了在常微分方程的三维耗散系统中吸引不变花托的存在性和规则性问题。我们的主要结果是一种构造性的计算机辅助证明方法，该方法适用于非扰动状态下的显式问题。根据圆环上的扩张率与圆环附近的收缩率之比，我们得出了吸引子规则性的可验证下界。我们分别考虑旋转和共振花托的两种重要情况。在旋转情况下，我们获得嵌入规则性的下限。在共振情况下，我们验证了仅存在$ C ^ 0 $且既不是星形也不是Lipschitz的tori的存在。