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February 28, 2026Journal of Nonlinear Mathematical Physics0 citationsOpen Access

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.

Abstract

In the present paper, we provide a weaker nondegenerate condition for the persistence of invariant tori in the parametrized forms for non-integrable Hamiltonian systems. This is a development of KAM following Salamon’s approach. Specifically, we establish a Rüssmann-type non-degeneracy condition for the non-integrable systems.

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