On Hölder's transformation

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概要

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• This paper investigates the main properties of Holder's transformation $\Hk_F$ of the contact space $\hat M$, generated by some function $F:\hat M\to\oR$, and its relation to Legendre's transformation $\Lk_H$. The commuting diagram $\Lk_H\circ\Hk_F=\Hk_W\circ\Lk_F$ and the related global properties of $\Hk$ and $\Lk$ are of particular interest. Holder's transformation can be used to transform Hamiltonian systems into Lie systems and Euler-Lagrange equations into Herglotz equations, this way establishing four equivalent pictures of the one-dimensional calculus of variations.

• 東京大学の論文

著者

• Hildebrandt Stefan

  Mathematisches Institut Der Universitat Bonn

関連論文

• On Hölder's transformation
• Uniqueness of stable minimal surfaces with partially free boundaries Dedicated to Robert Finn on the occasion of his seventieth birthday

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