Examples of nonintegrable analytic Hamiltonian vector fields with no small divisors

Author:
R. Cushman

Journal:
Trans. Amer. Math. Soc. **238** (1978), 45-55

MSC:
Primary 58F05; Secondary 70.58

MathSciNet review:
0478223

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Abstract: Any analytic symplectic diffeomorphism of a symplectic manifold *M* is the Poincaré map of a real analytic Hamiltonian vector field . If does not have an analytic integral, then has no analytic integral which is not a power series in *H*. Let . If has a finite contact homoclinic point, then is nonintegrable. Also Moser's polynomial mapping is nonintegrable.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1978-0478223-8

Keywords:
Symplectic diffeomorphism,
suspension,
integrable,
Moser's diffeomorphism,
homoclinic point

Article copyright:
© Copyright 1978
American Mathematical Society