Title: An alternative proof of infinite dimensional Gromov's non-squeezing for compact perturbations of linear maps Show Chinese title

Title: 线性映射的紧致扰动的无限维Gromov非压缩定理的另一种证明

Abstract: This paper deals with the problem of generalising Gromov's non squeezing theorem to an infinite dimensional Hilbert phase space setting. By following the lines of the proof by Hofer and Zehnder of finite dimensional non-squeezing, we recover an infinite dimensional non-squeezing result by Kuksin for symplectic diffeomorphisms which are non-linear compact perturbations of a symplectic linear map. We also show that the infinite dimensional non-squeezing problem, in full generality, can be reformulated as the problem of finding a suitable Palais-Smale sequence for a distinguished Hamiltonian action functional. Show Chinese abstract

Abstract: 本文讨论将Gromov的非压缩定理推广到无限维Hilbert相空间设置的问题。 通过遵循Hofer和Zehnder对有限维非压缩性证明的思路，我们恢复了Kuksin关于对称线性映射的非线性紧扰动的辛微分同胚的无限维非压缩结果。 我们还表明，在完全一般的情况下，无限维非压缩问题可以重新表述为寻找一个特定哈密顿作用泛函的合适Palais-Smale序列的问题。