PATH DEPENDENCE AND DIMENSIONAL EMERGENCEIN PROJECTIVE DYNAMICAL SYSTEMS
Автор: Khaled Bouzaiene
Загружено: 2026-01-17
Просмотров: 18
This research paper analyzes path dependence within projective dynamical systems by linking geometric movement to the algebraic structure of Lie brackets. The authors demonstrate that the discrepancy found when traversing a closed hexagonal path is exactly equal to the Lie bracket of the involved vector fields. This non-commutative behavior leads to dimensional emergence, where the rank of the system's Lie algebra filtration grows as a direct consequence of curvature. Furthermore, the study establishes that systems with specific spectral invariants and planar constraints naturally generate A2 root system geometry. Ultimately, the text provides a unified framework connecting holonomy, differential geometry, and topological rank growth to characterize how path-dependent discrepancies manifest in complex systems.
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