Question on energy displacement.

In summary, the conversation discusses how to show the energy displacement of Z^{2n}(r) is at most \pi r^2, with the use of Hofer's metric. The textbook of Mcduff and Salamon suggests identifying a two-dimensional ball with a square of the same area and then calculating the metric with a translation that does not intersect with the ball. The speaker is unsure of how to calculate the metric, but later finds the answer in Poletrovich's textbook.
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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].

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.
 
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  • #2
Never mind, I found the answer in Poletrovich's textbook, you got to love the internet...
 

FAQ: Question on energy displacement.

What is energy displacement?

Energy displacement is the transfer of energy from one location or form to another. It involves the movement of energy from a source to a receiver, resulting in a change in the energy state of the system.

What are some examples of energy displacement?

Some common examples of energy displacement include the conversion of chemical energy to heat energy in a fire, the transformation of electrical energy to light energy in a light bulb, and the transfer of kinetic energy to potential energy in a pendulum.

How is energy displacement measured?

Energy displacement can be measured in a variety of units depending on the type of energy being transferred. For example, electrical energy is measured in kilowatt-hours (kWh), while heat energy is measured in joules (J) or calories (cal). The specific unit of measurement will depend on the context and application.

What factors affect energy displacement?

The amount of energy displaced is influenced by a number of factors, including the efficiency of the energy transfer process, the distance between the source and receiver, and any resistances or obstacles that may impede the transfer of energy.

Why is energy displacement important?

Energy displacement is important because it is a fundamental process that allows for the functioning of various systems and processes in our world. It is also a key concept in understanding energy conservation and efficiency, as well as the impact of energy use on the environment.

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