具有两个耦合参数的双曲型vanDiejen系统的自对偶性和散射映射（附S。Ruijsenaars）
Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
摘要：
本文构造了一类双参数vanDiejen系统的整体作用角变量。根据Ruijsenaars关于平移不变模型的思想，所提出的作用角变量来自于对Lax矩阵所服从的对易关系的深入分析，而其规范性的证明是基于散射理论的研究。因此，我们表明，我们感兴趣的范Diejen系统是自对偶的因子化散射映射。在S. Ruijsenaars提出了一类指数型矩阵流谱渐近性的新证明。这一结果在我们的散射理论分析中是至关重要的。
英文摘要：
In this paper, we construct global action-angle variables for a certain two-parameter family of hyperbolic van Diejen systems. Following Ruijsenaars' ideas on the translation invariant models, the proposed action-angle variables come from a thorough analysis of the commutation relation obeyed by the Lax matrix, whereas the proof of their canonicity is based on the study of the scattering theory. As a consequence, we show that the van Diejen system of our interest is self-dual with a factorized scattering map. Also, in an appendix by S. Ruijsenaars, a novel proof of the spectral asymptotics of certain exponential type matrix flows is presented. This result is of crucial importance in our scattering-theoretical analysis.
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