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The concept of integrability on cantor sets for Hamiltonian systems

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Abstract

Differentiable Hamiltonian systems close to nondegenerate, integrable Hamiltonian systems are shown to be integrable on a Cantor set in the sense that on some Cantor set, (i) the invariant KAM-tori form a smooth foliation, (ii) there exist smooth, independent integrals in involution, and (iii) there exists a complete solution of the Hamilton Jacobi equation. The complement of the Cantor set is shown to be small in measure.

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  1. Mathematik, ETH-Zentrum, CH-8092, Zürich

    Jürgen Pöschel

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  1. Jürgen Pöschel
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Pöschel, J. The concept of integrability on cantor sets for Hamiltonian systems. Celestial Mechanics 28, 133–139 (1982). https://doi.org/10.1007/BF01230665

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