一类条件Cauchy方程P-构型的共轭性和非线性解
Conjugacy of P-configurations and nonlinear solutions to a certain conditional Cauchy equation
摘要：
我们研究一类特殊的动力系统，称为P-配置，和齐次柯西型函数方程的解的共轭之间的联系。我们发现，任何两个正则P-构形都可以通过同胚共轭，但不能通过同胚共轭。由此得到如下结论（解决了Paneah提出的一个公开问题）：函数方程f（t）= f（（t+1）/2）+ f（（t-1）/2），t \in [-1，1]存在连续非线性解.
英文摘要：
We study the connection between conjugations of a special kind of dynamical systems, called P-configurations, and solutions to homogeneous Cauchy type functional equations. We find that any two regular P-configurations are conjugate by a homeomorphism, but cannot be conjugate by a diffeomorphism. This leads us to the following conclusion (resolving an open problem posed by Paneah): there exist continuous nonlinear solutions to the functional equation: f(t) = f((t+1)/2) + f((t-1)/2), t \in [-1,1] .
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