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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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
May 13, 2022
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| In: |
Journal of fixed point theory and applications
Year: 2022, Volume: 24, Issue: 2, Pages: 1-32 |
| ISSN: | 1661-7746 |
| DOI: | 10.1007/s11784-022-00963-8 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s11784-022-00963-8
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| Author Notes: | Gabriele Benedetti and Jungsoo Kang |
| Summary: | 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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| Item Description: | Dedicated to Prof. Claude Viterbo on the occasion of his 60th birthday Gesehen am 20.07.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1661-7746 |
| DOI: | 10.1007/s11784-022-00963-8 |