I want to show that the energy displacement of [itex]Z^{2n}(r)[/itex], the 2n-dimensional cylinder with radial radius is at most [itex]\pi r^2[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

In the textbook of Mcduff and Salamon they write that I should identify the two dimensional ball (with radius r) with a square of the same area, and then calculate Hofer's metric, [itex]d_H(Id,ϕ)[/itex] where ϕ is a translation s.t ϕ(B2(r)×K)∩(B2(r)×K)=∅, where [itex]K \subset \mathbb{R}^{2n-2}[/itex].

I don't know how to calculate Hofer's metric, I mean it depends on the Hamiltonian here, and I don't know how does it look here?

Thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question on energy displacement.

**Physics Forums | Science Articles, Homework Help, Discussion**