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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Entropy and completely integrable Hamiltonian systems
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by Gabriel Paternain
Proc. Amer. Math. Soc. 113 (1991), 871-873
DOI: https://doi.org/10.1090/S0002-9939-1991-1059632-7
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Abstract:

Let $H$ be a Hamiltonian on a four-dimensional symplectic manifold. Suppose the system is completely integrable and on some nonsingular compact level surface $Q$ the integral is such that the connected components of the set of critical points form submanifolds. Then we prove that the topological entropy of the system restricted to $Q$ is zero. As a corollary we deduce the nonexistence of completely integrable geodesic flows by means of integrals as described above for compact surfaces with negative Euler characteristic.
References
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Bibliographic Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 871-873
  • MSC: Primary 58F17; Secondary 58F05
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1059632-7
  • MathSciNet review: 1059632