2 results
Escaping orbits are rare in the quasi-periodic Fermi–Ulam ping-pong
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 40 / Issue 4 / April 2020
- Published online by Cambridge University Press:
- 06 September 2018, pp. 975-991
- Print publication:
- April 2020
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Rigidity of Hamiltonian Actions
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- Journal:
- Canadian Mathematical Bulletin / Volume 46 / Issue 2 / 01 June 2003
- Published online by Cambridge University Press:
- 20 November 2018, pp. 277-290
- Print publication:
- 01 June 2003
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This paper studies the following question: Given an
${\omega }'$-symplectic action of a Lie group on a manifold 
$M$ which coincides, as a smooth action, with a Hamiltonian 
$\omega$-action, when is this action a Hamiltonian ${\omega }'$-action? Using a result of Morse-Bott theory presented in Section 2, we show in Section 3 of this paper that such an action is in fact a Hamiltonian ${\omega }'$-action, provided that $M$ is compact and that the Lie group is compact and connected. This result was first proved by Lalonde-McDuff-Polterovich in 1999 as a consequence of a more general theory that made use of hard geometric analysis. In this paper, we prove it using classical methods only.
