This work develops a functional analytic framework for making computer assisted arguments involving transverse heteroclinic connecting orbits between hyperbolic periodic solutions of ordinary differential equations. We exploit a Fourier-Taylor approximation of the local stable/unstable manifold of the periodic orbit, combined with a numerical method for solving two point boundary value problems via Chebyshev series approximations. The a-posteriori analysis developed provides mathematically rigorous bounds on all approximation errors, providing both abstract existence results and quantitative information about the true heteroclinic solution. Example calculations are given for both the dissipative Lorenz system and the Hamiltonian Hill Restricted Four Body Problem.

翻译：本文发展了一种泛函分析框架，用于对常微分方程双曲周期解之间的横向异宿连接轨道进行计算机辅助论证。我们利用周期轨道的局部稳定/不稳定流形的傅里叶-泰勒近似，结合通过切比雪夫级数近似求解两点边值问题的数值方法。所发展的后验分析提供了所有近似误差的数学严格界，既给出了抽象存在性结果，又提供了真实异宿解的定量信息。文中以耗散洛伦兹系统和哈密顿希尔限制四体问题为例进行了计算演示。