In this paper, we consider the existence of analytic invariant curves of an iterative equation

$$f(f(x)) = x{{\rm{e}}^{a - x - f(x)}}$$

which arises from Ricker-type second-order equation. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the parameter at resonance, i.e., at a root of the unity, but also the parameter near resonance under the Brjuno condition.

中文翻译：

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与 Ricker 型二阶方程相关的迭代方程的解析不变曲线

在本文中，我们考虑迭代方程的解析不变曲线的存在性

$$f(f(x)) = x{{\rm{e}}^{a - x - f(x)}}$$

由 Ricker 型二阶方程产生。通过将施罗德变换方程化简为辅助方程，作者不仅讨论了共振时的参数，即单位根处的参数，还讨论了Brjuno条件下共振附近的参数。