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arXiv 1807.094612018-07math.DSmath.SG

非凸马瑟理论与托氏圆柱的康利猜想

Non-convex Mather's theory and the Conley conjecture on the cotangent bundle of the torus

Claude Viterbo

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AI总结：

本文通过辛同调化方法证明了非凸马瑟理论中关于圆柱的康利猜想及周期轨道的存在性。

摘要：

本文旨在利用辛同调化方法（见[V4]）证明存在周期轨道和具有旋转数依赖于同调化哈密顿量微分的不变测度。我们还证明了在圆柱的cotangent bundle上的康利猜想。两个证明均依赖于辛同调化及其改进。

英文摘要：

The aim of this paper is to use the methods and results of symplectic homogenization (see [V4]) to prove existence of periodic orbits and invariant measures with rotation number depending on the differential of the Homogenized Hamiltonian. We also prove the Conley conjecture on the cotangent bundle of the torus. Both proofs rely on Symplectic Homogenization and a refinement of it.

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