The Persistence of Invariant Tori in a Parametric Setting

Key Points

• The aim is to establish a weaker non-degenerate condition for the persistence of invariant tori in non-integrable Hamiltonian systems.
• Develop a non-degenerate condition based on KAM theory.
• Utilize a Rüssmann-type framework for analysis.
• Investigate parametric forms of Hamiltonian systems.
• Present a new condition that broadens the applicability of traditional KAM results.
• Support the idea that invariant tori can persist under certain parametric variations.