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Analytic Invariant Curves for an Iterative Equation Related to Ricker-type Second-order Equation
Acta Mathematica Sinica, English Series ( IF 0.8 ) Pub Date : 2021-07-15 , DOI: 10.1007/s10114-021-8530-x Hou Yu Zhao 1 , Michal Fečkan 2, 3
中文翻译:
与 Ricker 型二阶方程相关的迭代方程的解析不变曲线
更新日期:2021-07-27
Acta Mathematica Sinica, English Series ( IF 0.8 ) Pub Date : 2021-07-15 , DOI: 10.1007/s10114-021-8530-x Hou Yu Zhao 1 , Michal Fečkan 2, 3
Affiliation
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:
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。