The Geometry of Asymmetric Network Flows: Symplectic Leaves, Maslov Spectra, and Geodesic Instability on so(n)

Key Points

• The study aims to explore the geometric structure of asymmetric network flows and their implications on stability and dynamics.
• Analysis of symplectic leaves within network flows.
• Investigation of Maslov spectra related to geodesic paths.
• Theoretical framework applied to so(n) for understanding flow dynamics.
• Identified key geometric characteristics that influence flow stability.
• Demonstrated connections between symplectic geometry and network behavior.
• Revealed new insights into geodesic instability related to network configurations.