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<p>Kolmogorov – Arnold – Moser theory started in the 1950s as theperturbation theory for persistence of multi- orquasi-periodic motions in Hamiltonian systems.Since then the theory obtained a branch where the persistentoccurrence of quasi-periodicity is studied in variousclasses of systems, which may depend on parameters.The view changed into the direction of structural stability,concerning the occurrence of quasi-periodic tori on a setof positive Hausdorff measure in a sub-manifold of theproduct of phase space and parameter space.This paper contains an overview of this development withan emphasis on the world of dissipative systems, wherefamilies of quasi-periodic tori occur and bifurcate in apersistent way.The transition from orderly to chaotic dynamics here formsa leading thought.</p>

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Parametrised KAM Theory, an Overview

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Henk W. Broer,
  • Heinz Hanßmann,
  • Florian Wagener

摘要

Kolmogorov – Arnold – Moser theory started in the 1950s as theperturbation theory for persistence of multi- orquasi-periodic motions in Hamiltonian systems.Since then the theory obtained a branch where the persistentoccurrence of quasi-periodicity is studied in variousclasses of systems, which may depend on parameters.The view changed into the direction of structural stability,concerning the occurrence of quasi-periodic tori on a setof positive Hausdorff measure in a sub-manifold of theproduct of phase space and parameter space.This paper contains an overview of this development withan emphasis on the world of dissipative systems, wherefamilies of quasi-periodic tori occur and bifurcate in apersistent way.The transition from orderly to chaotic dynamics here formsa leading thought.