https://doi.org/10.1140/epjp/s13360-024-05000-w
Regular Article
Chaotic dynamics and zero distribution: implications and applications in control theory for Yitang Zhang’s Landau Siegel zero theorem
1
Department of Mathematics, University of Batna 2, Mostefa Ben Boulaïd 53, 05078, Route de Constantine, Fésdis, Batna, Algeria
2
Universidad Nacional de Colombia, Departamento de Matemáticas, Bogotá, Colombia
Received:
29
October
2023
Accepted:
12
February
2024
Published online:
4
March
2024
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.
A correction to this article is available online at https://doi.org/10.1140/epjp/s13360-024-05117-y.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
