论文标题
扰动任何完全集成的汉密尔顿系统的关键思想，获得卷熵的非专注
Key ideas behind perturbing any completely integrable Hamiltonian system obtaining volume entropy non-expansiveness
论文作者
论文摘要
本文宣布了结果，随后对背后的一些想法进行了解释。证明将出现在其他地方。我们的目标是建造任何完全可以集成的哈密顿制度的哈密顿扰动，其自由度为$ 2n $（$ n \ geq 2 $）。扰动为$ c^{\ infty} $ smill，但所产生的流量为阳性度量熵，并且满足KAM非分类条件。关键点是，可以在一个轨迹的任意小管邻居中生成阳性熵。
This paper is an announcement of a result followed with explanations of some ideas behind. The proofs will appear elsewhere. Our goal is to construct a Hamiltonian perturbation of any completely integrable Hamiltonian system with $2n$ degrees of freedom ($n\geq 2$). The perturbation is $C^{\infty}$ small but the resulting flow has positive metric entropy and it satisfies KAM non-degeneracy conditions. The key point is that positive entropy can be generated in an arbitrarily small tubular neighborhood of one trajectory.
