科研之友
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摘要
We use the Hofer norm to show that all Hamiltonian diffeomorphisms with compact support in R-2n that displace an open connected set with a nonzero Hofer-Zehnder capacity move a point farther than a capacity-dependent constant. In R-2, this result is extended to all compactly supported area-preserving homeomorphisms. Next, using the spectral norm, we show the result holds for Hamiltonian diffeomorphisms on closed surfaces. We then show that all area-preserving homeomorphisms of S-2 and RP2 that displace the closure of an open connected set of fixed area move a point farther than an area-dependent constant.
- 出版日期2013
