创新动力学：利用 Perelman 熵与 Ricci 流构建流形上的星体位置模型
Innovative Dynamics: Utilizing Perelman's Entropy and Ricci Flow for Settler Position Models on Manifolds
AI总结：
本文提出一种基于离散动力系统、Ricci 流和 Perelman 熵的恒星位置混沌建模方法，通过 Lyapunov 指数与分岔分析揭示其动力学特性，并证明熵呈指数增长导致长期位置预测难度增加。
摘要：
本文探索了一种利用离散动力系统对恒星位置动力学进行建模的新方法。我们通过基于赤经、赤纬和距离的离散时间更新规则来定义恒星演化，并借助非线性函数和外部扰动引入混沌行为。通过应用 Ricci 流和黎曼度量，我们为恒星位置动力学提供了新的见解。利用 Perelman 熵的理论计算来评估系统复杂性，并采用高精度 Runge-Kutta 方法确保混沌模型的精确求解。我们使用 Lyapunov 指数量化混沌，并进行分岔分析以研究参数变化如何影响动力学。将我们的模型与 Lorenz 吸引子进行比较，揭示了恒星动力学中的相似性和独特特征。结果表明，熵呈指数增长，表明随着时间推移，精确预测恒星位置变得越来越困难。本研究通过将混沌理论与天文学建模相结合，增进了对天体系统中混沌的理解，并为动力系统理论做出了贡献。
英文摘要：
This paper explores a novel approach to modeling the positional dynamics of stars using discrete dynamical systems. We define star evolution through discrete-time update rules based on right ascension, declination, and distance, incorporating chaotic behavior via nonlinear functions and external perturbations. By applying Ricci flow and Riemannian metrics, we provide new insights into the positional dynamics of stars. Theoretical computations of Perelman entropy are used to assess system complexity, with high-precision Runge-Kutta methods ensuring accurate solutions for our chaotic model. We quantify chaos using Lyapunov exponents and perform bifurcation analysis to study how parameter variations affect the dynamics. Comparing our model to the Lorenz attractor reveals both similarities and unique characteristics in stellar dynamics. Our results show that entropy increases exponentially, indicating that predicting star positions with precision becomes increasingly challenging over time. This study advances the understanding of chaos in celestial systems and contributes to dynamical systems theory by integrating chaos theory with astronomical modeling.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
