论文标题
关于浮子条形码的生长
On the growth of the Floer barcode
论文作者
论文摘要
本文是作者最近关于条形码熵的工作的后续。我们研究了浮子络合物的条形码的生长，用于紧凑型的哈密顿型差异性。特别是，我们引入了具有类似条形码熵的特性的顺序条形码熵，从上方界定它，并且对条形码生长更敏感。我们证明，在两个方面，顺序条形码熵等于拓扑熵，因此等于普通的条形码熵。我们还研究了迭代下$γ$ norm的行为。我们表明，当地图具有足够多的双曲周期点时，迭代元素的$γ$ norm与零分开，因此，它与零$ c^\ infty $分离为二维。我们还涉及伪旋转的条形码熵的性质，更一般而言，最多是$γ$的周期性地图。
This paper is a follow up to the authors' recent work on barcode entropy. We study the growth of the barcode of the Floer complex for the iterates of a compactly supported Hamiltonian diffeomorphism. In particular, we introduce sequential barcode entropy which has properties similar to barcode entropy, bounds it from above and is more sensitive to the barcode growth. We prove that in dimension two the sequential barcode entropy equals the topological entropy and hence equals the ordinary barcode entropy. We also study the behavior of the $γ$-norm under iterations. We show that the $γ$-norm of the iterates is separated from zero when the map has sufficiently many hyperbolic periodic points and, as a consequence, it is separated from zero $C^\infty$-generically in dimension two. We also touch upon properties of the barcode entropy of pseudo-rotations and, more generally, $γ$-almost periodic maps.
