Title: Renormalization group based implicit function approach to connecting orbits Show Chinese title

Title: 基于重整化群的隐函数方法连接轨道

Abstract: Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on renormalization group, an implicit function scheme is designed to effectively represent connections of disparate types, where coefficients of the defining function satisfy a set of linear algebraic equations, which greatly simplifies their computation. Unknown system parameters are conveniently determined by minimizing an error function. Symmetry may be profitably utilized to reduce the computation load. Homoclinic or heteroclinic connections are found in five popular examples approximately or exactly, demonstrating the effectiveness of the new scheme. Show Chinese abstract

Abstract: 连接轨道是非线性系统状态空间中的重要不变结构，已经设计了各种技术来计算它们。 然而，对整个轨道的统一解析近似似乎很少见。 在这里，基于重整化群，设计了一种隐函数方案，以有效表示不同类型的连接，其中定义函数的系数满足一组线性代数方程，这大大简化了它们的计算。 未知系统参数可以通过最小化误差函数方便地确定。 对称性可以被有利地利用来减少计算负担。 在五个流行的例子中发现了同宿或异宿连接，近似或精确地展示了新方案的有效性。