Holonomic Derivative-Order Geometry: Companion Transport, Projective Packet Closure, and WKB Fingerprints

Key Points

• This work aims to expand the derivative-order program to include holonomic packets and analyze their dynamics.
• Developed an exact companion transport for holonomic derivative-order packets.
• Established a projective closure that describes packet closure in projective space.
• Derived second-order dynamics for packet evolution.
• Obtained a WKB-type fingerprint encoding the asymptotic behavior of holonomic packets.
• Introduced new tools for analyzing holonomic derivative-order geometry.
• Demonstrated systematic connections between holonomic packets and WKB methods.
• Revealed insights into projective packet dynamics.

Abstract