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Talk:Kolmogorov-Arnold-Moser theory - Scholarpedia

Talk:Kolmogorov-Arnold-Moser theory

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    A Reviewer made the following comment regarding the term "proper degeneracy"

    <review>I think this is just the notion of a degenerate system, but not necessarily of a properly degenerate one. In my understanding of Arnold's paper, proper degeneracy means that a degenerate system becomes nondegenerate by incorporating the average of the perturbation to first order and pushing the remaining perturbation to second order. </review>

    However, the common usage of "proper degeneracy" is just that of an integrable system having the Hamiltonian in action variables, whose hessian matrix has an identically vanishing determinant; compare, e.g., [V.I. Arnold, V.V. Kozlov and A.I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, Third Edition, Springer 2006, Sec. 5.2.1, p. 181

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