Relative Hofer-Zehnder capacity and positive symplectic homology
We study the relationship between a homological capacity cSH+ (W ) for Liouville domains W defined using positive symplectic homology and the existence of periodic orbits for Hamiltonian systems on W: if the positive symplectic homology of W is non-zero, then the capacity yields a finite upper bound...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
May 13, 2022
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| In: |
Journal of fixed point theory and applications
Year: 2022, Jahrgang: 24, Heft: 2, Pages: 1-32 |
| ISSN: | 1661-7746 |
| DOI: | 10.1007/s11784-022-00963-8 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s11784-022-00963-8
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| Verfasserangaben: | Gabriele Benedetti and Jungsoo Kang |
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| 500 | |a Dedicated to Prof. Claude Viterbo on the occasion of his 60th birthday | ||
| 500 | |a Gesehen am 20.07.2022 | ||
| 520 | |a We study the relationship between a homological capacity cSH+ (W ) for Liouville domains W defined using positive symplectic homology and the existence of periodic orbits for Hamiltonian systems on W: if the positive symplectic homology of W is non-zero, then the capacity yields a finite upper bound to the π1 sensitive Hofer-Zehnder capacity of W relative to its skeleton and a certain class of Hamiltonian diffeomorphisms of W has infinitely many non-trivial contractible periodic points. En passant, we give an upper bound for the spectral capacity of W in terms of the homological capacity cSH(W ) defined using the full symplectic homology. Applications of these statements to cotangent bundles are discussed and use a result by Abbondandolo and Mazzucchelli in the appendix, where the monotonicity of systoles of convex Riemannian two-spheres in R3 is proved. | ||
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| 650 | 4 | |a Liouville domains | |
| 650 | 4 | |a periodic orbits of Hamiltonian systems | |
| 650 | 4 | |a symplectic homology | |
| 700 | 1 | |a Kang, Jungsoo |e VerfasserIn |0 (DE-588)1221837737 |0 (DE-627)174027914X |4 aut | |
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