Geometry of almost-conserved quantities in symplectic maps

Key Points

• The geometric properties of almost-conserved quantities are outlined in the context of symplectic maps, emphasizing their significance in Hamiltonian dynamics.
• Specific relationships between these quantities in phase space illustrate their near-conservation and stability behavior over time.
• Observational analysis focusing on phase space transformations reveals unexpected structure related to these quantities.
• Insights gained elucidate the implications of these geometric aspects across broader Hamiltonian systems.