On variants of Arnold conjecture

Roman Golovko

Archivum Mathematicum (2020)

  • Volume: 056, Issue: 5, page 277-286
  • ISSN: 0044-8753

Abstract

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In this note we discuss the collection of statements known as Arnold conjecture for Hamiltonian diffeomorphisms of closed symplectic manifolds. We provide an overview of the homological, stable and strong versions of Arnold conjecture for non-degenerate Hamiltonian systems, a few versions of Arnold conjecture for possibly degenerate Hamiltonian systems, the degenerate version of Arnold conjecture for Hamiltonian homeomorphisms and Sandon’s version of Arnold conjecture for contactomorphisms.

How to cite

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Golovko, Roman. "On variants of Arnold conjecture." Archivum Mathematicum 056.5 (2020): 277-286. <http://eudml.org/doc/297198>.

@article{Golovko2020,
abstract = {In this note we discuss the collection of statements known as Arnold conjecture for Hamiltonian diffeomorphisms of closed symplectic manifolds. We provide an overview of the homological, stable and strong versions of Arnold conjecture for non-degenerate Hamiltonian systems, a few versions of Arnold conjecture for possibly degenerate Hamiltonian systems, the degenerate version of Arnold conjecture for Hamiltonian homeomorphisms and Sandon’s version of Arnold conjecture for contactomorphisms.},
author = {Golovko, Roman},
journal = {Archivum Mathematicum},
keywords = {Arnold conjecture; fixed points; Hamiltonian symplectomorphisms},
language = {eng},
number = {5},
pages = {277-286},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On variants of Arnold conjecture},
url = {http://eudml.org/doc/297198},
volume = {056},
year = {2020},
}

TY - JOUR
AU - Golovko, Roman
TI - On variants of Arnold conjecture
JO - Archivum Mathematicum
PY - 2020
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 056
IS - 5
SP - 277
EP - 286
AB - In this note we discuss the collection of statements known as Arnold conjecture for Hamiltonian diffeomorphisms of closed symplectic manifolds. We provide an overview of the homological, stable and strong versions of Arnold conjecture for non-degenerate Hamiltonian systems, a few versions of Arnold conjecture for possibly degenerate Hamiltonian systems, the degenerate version of Arnold conjecture for Hamiltonian homeomorphisms and Sandon’s version of Arnold conjecture for contactomorphisms.
LA - eng
KW - Arnold conjecture; fixed points; Hamiltonian symplectomorphisms
UR - http://eudml.org/doc/297198
ER -

References

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