论文标题
在$ \ mathbb {c} \ text {p}^d $上的hofer-zehnder上，通过生成函数（带有egor shelukhin的附录）
On the Hofer-Zehnder conjecture on $\mathbb{C}\text{P}^d$ via generating functions (with an appendix by Egor Shelukhin)
论文作者
论文摘要
我们使用Givental，Théret和我们自己开发的生成功能技术来推论$ \ Mathbb {c} \ text {p}^d $ franks sellukhin引起的弗兰克斯定理的同源性概括。该结果尤其证明了在非分类情况下的Hofer-Zehnder猜想：$ \ Mathbb {c} \ text {p}^d $的每一个汉密尔顿的差异性，至少具有至少$ d+2 $ de-2 $ demented not-degenerated Points的周期点具有无限的周期性点。我们的证明不吸引浮动同源性或$ j $ holomormorphic曲线的理论。 Shelukhin撰写的附录包含了史密斯型不平等的新证明，这是由于浮动理论引起的汉密尔顿二型差异性的条形码，该理论使自己适应生成功能的设置。
We use generating function techniques developed by Givental, Théret and ourselves to deduce a proof in $\mathbb{C}\text{P}^d$ of the homological generalization of Franks theorem due to Shelukhin. This result proves in particular the Hofer-Zehnder conjecture in the non-degenerated case: every Hamiltonian diffeomorphism of $\mathbb{C}\text{P}^d$ that has at least $d+2$ non-degenerated periodic points has infinitely many periodic points. Our proof does not appeal to Floer homology or the theory of $J$-holomorphic curves. An appendix written by Shelukhin contains a new proof of the Smith-type inequality for barcodes of Hamiltonian diffeomorphisms that arise from Floer theory, which lends itself to adaptation to the setting of generating functions.
