通过对称性实现球面上面积保全映射的霍弗增长二分法

arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-16 DOI:arxiv-2408.08854

Lev Buhovsky, Ben Feuerstein, Leonid Polterovich, Egor Shelukhin

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引用次数: 0

摘要

我们证明了二球体上的自发哈密顿流表现出以下二分法：霍弗规范要么线性增长，要么在时间上受一个普遍常数 C 的约束。从本质上讲，我们证明了每一个自发的哈密顿非同形都与霍弗公设中的一个元素 C 共轭，该元素与高度的一个函数生成的元素 C 接近。

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A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization

We prove that autonomous Hamiltonian flows on the two-sphere exhibit the following dichotomy: the Hofer norm either grows linearly or is bounded in time by a universal constant C. Our approach involves a new technique, Hamiltonian symmetrization. Essentially, we prove that every autonomous Hamiltonian diffeomorphism is conjugate to an element C-close in the Hofer metric to one generated by a function of the height.

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arXiv - MATH - Symplectic Geometry

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