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<p>In this note, we briefly discuss how the singular KAM theory of [<CitationRef CitationID="CR7">7</CitationRef>] — which was worked out for the mechanical case <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\frac{1}{2}|y|^{2}+\varepsilon f(x)\)</EquationSource> </InlineEquation> — can be extended to <i>convex</i> real-analyticnearly integrable Hamiltonian systemswith Hamiltonian in action-angle variables given by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(h(y)+\varepsilon f(x)\)</EquationSource> </InlineEquation> with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(h\)</EquationSource> </InlineEquation> convex and<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> generic.</p>

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Singular KAM Theory for Convex Hamiltonian Systems

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Santiago Barbieri,
  • Luca Biasco,
  • Luigi Chierchia,
  • Davide Zaccaria

摘要

In this note, we briefly discuss how the singular KAM theory of [7] — which was worked out for the mechanical case \(\frac{1}{2}|y|^{2}+\varepsilon f(x)\) — can be extended to convex real-analyticnearly integrable Hamiltonian systemswith Hamiltonian in action-angle variables given by \(h(y)+\varepsilon f(x)\) with \(h\) convex and \(f\) generic.