周期行波谱随周期趋于无穷大而收敛于同宿极限的本质谱
Convergence as period goes to infinity of spectra of periodic traveling waves toward essential spectra of a homoclinic limit
摘要：
我们重新审视R. A.加德纳的收敛频谱的周期性行波同宿，或无限周期的限制，延长他的结果的情况下，基本的，而不是点谱的限制同宿波。值得注意的是，收敛到基本频谱被认为是代数率相对于周期相比，指数收敛速率的点谱。在分析过程中，我们不仅证明了谱的收敛性，而且证明了相应的周期Evans函数的适当重整化对于同宿极限波的Evans函数的收敛性，这一事实对于数值研究是有用的
英文摘要：
We revisit the analysis by R.A. Gardner of convergence of spectra of periodic traveling waves in the homoclinic, or infinite-period limit, extending his results to the case of essential rather than point spectra of the limiting homoclinic wave. Notably, convergence to essential spectra is seen to be of algebraic rate with respect to period as compared to the exponential rate of convergence to point spectra. In the course of the analysis, we show not only convergence of spectrum but also convergence of an appropriate renormalization of the associated periodic Evans function to the Evans function for the limiting homoclinic wave, a fact that is useful for numerical investigations
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