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Almost existence from the feral perspective and some questions

Part of: Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Symplectic geometry, contact geometry Complex manifolds Smooth dynamical systems: general theory

Published online by Cambridge University Press:  10 June 2021

JOEL W. FISH  and
HELMUT H. W. HOFER Open the ORCID record for HELMUT H. W. HOFER [Opens in a new window]
JOEL W. FISH*
Affiliation:
Department of Mathematics, University of Massachusetts Boston, Boston, MA, USA
HELMUT H. W. HOFER
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, NJ, USA (e-mail: hofer@math.ias.edu)
*
e-mail: joel.fish@umb.edu
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Abstract

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.

Keywords

feral curvesalmost existenceadiabatic

MSC classification

Primary: 32Q65: Pseudoholomorphic curves 37C99: None of the above, but in this section 37J99: None of the above, but in this section
Secondary: 53D99: None of the above, but in this section
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 2: Anatole Katok Memorial Issue Part 1: Special Issue of Ergodic Theory and Dynamical Systems , February 2022 , pp. 792 - 834
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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