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arXiv · 2310.14127

Chaotic Dynamics and Zero Distribution: Implications and Applications in Control Theory for Yitang Zhang's Landau Siegel Zero Theorem

Zeraoulia Rafik·Alvaro Humberto Salas
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Abstract

This study delves into the realm of chaotic dynamics derived from Dirichlet L-functions, drawing inspiration from Yitang Zhang's groundbreaking work on Landau-Siegel zeros. The dynamic behavior reveals profound chaos, corroborated by the calculated Lyapunov exponents and entropy, attesting to the system's inherent unpredictability. Furthermore, we establish a novel connection between Fractal geometry and Quantum chaos, predicting the distributions of zeros for both Yitang dynamics and Riemann dynamics. These findings offer indirect support for Zhang's groundbreaking theorem concerning Landau-Siegel zeros and suggest that these chaotic dynamics could find application in engineering and control systems, demonstrating the potential to harness chaos for beneficial purposes. The exploration of stability within electrical systems further uncovers the instability of fixed points, highlighting both the challenges and opportunities for harnessing chaotic behavior to achieve specific control objectives. This study not only contributes to our understanding of chaotic dynamics but also opens new avenues for exploring the potential applications of Yitang dynamics in the field of electrical control systems. It paves the way for innovative approaches to address real-world engineering challenges and may be considered as a new consequence for the generalized Riemann hypothesis.

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Zeraoulia Rafik, Alvaro Humberto Salas. 2023-10-21. Chaotic Dynamics and Zero Distribution: Implications and Applications in Control Theory for Yitang Zhang's Landau Siegel Zero Theorem. https://doi.org/10.1140/epjp%2Fs13360-024-05000-w

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