The Concept of Integrability on Cantor Sets for Hamiltonian Systems

Details The Concept of Integrability on Cantor Sets for Hamiltonian Systems The Concept of Integrability on Cantor Sets for Hamiltonian Systems

Sep 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28..133p&link_type=abstract

Celestial Mechanics, Volume 28, Issue 1-2, pp. 133-139

Computer Science

Scientific paper

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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