AI 中文总结
研究一般光滑扩张映射的共振态性质，证明其共振简单且零是正则值，实值共振态是莫尔斯函数，还利用纳什 - 莫泽理论得出足够大度映射的共振态与一般光滑函数有相同性质。
AI 中文摘要
我们证明了一般光滑扩张映射的共振是简单的，并且零是相关共振态的正则值。此外，实值共振态是莫尔斯函数。利用纳什 - 莫泽理论，我们还证明了足够大度数（取决于映射作用的流形维度）的一般光滑扩张映射的共振态与一般光滑函数具有相同性质。
英文摘要
We prove that the resonances for a generic smooth expanding map are simple and that zero is a regular value for the associated resonant states. Moreover, the real-valued resonant states are Morse functions. Using Nash-Moser theory, we also prove that the resonant states for a generic smooth expanding map of large enough degree (depending on the dimension of the manifold the map is acting on) have the same properties as generic smooth functions.
Commentsv2: fixed a mistake in the proof of Lemma 6.11
