动力系统第一本征函数的半经典极限与回归集的集中度
Semi-classical limits of the first eigenfunction and concentration on the recurrent sets of a dynamical system
摘要：
亲爱的读者，请找到第三和最后一部分的一系列文件的奇异摄动的第一本征函数相关的非自伴二阶椭圆算子。这个系列始于1999年，我们于2000年在哥伦比亚大学展示了早期结果。我们在2001年和2005年的CRAS上发表了两篇论文，总结了我们的研究结果。本文包含了已宣布的定理的证明和许多未解决的问题。我们试图在顶级数学期刊（Annals，Acta，Duke.）上发表这些结果。但我们的研究结果对他们来说不够有趣，可能也不够时髦。你们中的一些人可能喜欢这个工作，所以它在这里。最好的问候，伊万和大卫。研究了紧致黎曼流形上正二阶算子的第一本征函数在扩散常数$ε$趋于零时的半经典极限.如果扩散的漂移由Morse-Smale向量场$b$给出，则本征函数的极限集中在$b$的递归集上。爆破分析使我们能够找到循环集上极限测度的主要性质。
英文摘要：
Dear Reader, please find the third and last part of a series of papers on the singular perturbation of the first eigenfunction associated to a non self-adjoint second order elliptic operators. This series started in 1999 and we presented the early results in 2000 at Columbia University. We published two notes in CRAS in 2001 and 2005 summarizing our results. The present paper contains the proofs of the announced theorems and many open questions. We tried to publish these results in the the top tier of mathematical journals (Annals, Acta, Duke...) but our results were not deemed sufficiently interesting for them and probably not trendy enough. Some of you may like this work, so here it is. Best Regards, Ivan and David. We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold, when the diffusion constant $ε$ goes to zero. If the drift of the diffusion is given by a Morse-Smale vector field $b$, the limits of the eigenfunctions concentrate on the recurrent set of $b$. A blow-up analysis enables us to find the main properties of the limit measures on a recurrent set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
