经济增长理论中的同时同调性与双哈密顿结构
Simultaneous Holotheticity and Bi-Hamiltonian Structures in Economic Growth Theory
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中文总结 AI 辅助
本文将双哈密顿结构等几何框架应用于经济增长理论，运用同时同调性原理构建三类增长模式的层级分类，研究容量受限下的结构边界危机，揭示经济轨迹遇资源上限时的泊松笔秩坍缩现象。
中文摘要 AI 辅助
本文建立了一个严谨的几何框架，将有限维双哈密顿结构和南布-泊松力学的形式架构应用于宏观经济增长理论。我们超越静态经验相关性，运用Ryuzo Sato的同时同调性原理，证明经济生产函数天然作为可积流的稳定、与时间无关的几何叶出现。我们构建了三种基本经济增长模式的统一层级分类，这些模式依次推广：经典无约束的柯布-道格拉斯模式、资源受限的S型生态系统响应、以及容量受限的“过度调整与崩溃”模式。此外，我们将该范式推进到非光滑领域，研究当总经济轨迹遇到明确的资源承载能力上限时发生的结构边界危机，表明这些容量极限会诱导相容逆变泊松笔发生灾难性秩坍缩。
英文摘要
In this paper, we establish a rigorous geometric framework that applies the formal architecture of finite-dimensional bi-Hamiltonian structures and Nambu-Poisson mechanics to macroeconomic growth theory. Moving beyond static empirical correlations, we deploy Ryuzo Sato's principle of simultaneous holotheticity to demonstrate that economic production functions emerge natively as stable, time-independent geometric leaves of integrable flows. We construct a unified, hierarchical taxonomy of three fundamental economic growth regimes that sequentially generalize one another: the classical, unconstrained Cobb-Douglas mode; the resource-limited S-shaped econsystem response; and the capacity-bounded "overshoot-and-collapse" regime. Furthermore, we push this paradigm into non-smooth territory by investigating the structural boundary crises that occur when aggregate economic trajectories encounter definitive resource carrying capacity ceilings. We show that these capacity limits induce a catastrophic rank-collapse of the compatible contravariant Poisson pencil.
