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almost existence

Ergodic Theory and Dynamical Systems (1)

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Almost existence from the feral perspective and some questions
Part of
JOEL W. FISH, HELMUT H. W. HOFER
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 2 / February 2022

Published online by Cambridge University Press:

10 June 2021, pp. 792-834

Print publication:

February 2022
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We use feral pseudoholomorphic curves and adiabatic degeneration to prove an extended version of the so-called ‘almost existence result’ for regular compact Hamiltonian energy surfaces. That is, that for a variety of symplectic manifolds equipped with a Hamiltonian, almost every (non-empty) compact energy level has a periodic orbit.