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Relative Hofer-Zehnder capacity and positive symplectic homology
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- Authors
- Issue Date
- 2022-06
- Publisher
- SPRINGER BASEL AG
- Citation
- Journal of Fixed Point Theory and Applications, Vol.24 No.2
- Abstract
- We study the relationship between a homological capacity c(SH+) (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 pi(1)-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 c(SH)(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 R-3 is proved.
- ISSN
- 1661-7738
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