LP-Conjugation: Unraveling Time Series Dynamics through Chaotic Map Convolution

LP-Conjugation, introduced by Padua and Libao, is a versatile method used in solving the Inverse Frobenius-Perron problem (IFPP) for chaotic systems based on time series data. While their initial work focused on the logistic map and prime gap data, this article highlights the broader significance of LP-Conjugation as a powerful tool for the IFPP. Any chaotic map can be employed with established chaotic time series data to reconstruct unknown maps. LP-Conjugation utilizes a known chaotic map ?(?) and invariant distribution F(?) to construct an unknown chaotic map ?(?) with known invariant distribution H(?). The article presents a detailed proof, illustrating the method's robustness and adaptability. Further illustrations on how to construct a chaotic map from this logistic-based chaotic map sample is also provided.  Real-world examples demonstrate LP-Conjugation's efficacy in diverse applications, solidifying its role as a valuable approach for solving the IFPP and understanding chaotic dynamics.