用生成函数论$\mathbb{C} \ mathm {P}^d$的哈密顿微分同态的周期点

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Symplectic Geometry Pub Date : 2020-04-05 DOI:10.4310/JSG.2022.v20.n1.a1

Simon Allais

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引用次数: 6

摘要

在gigiental和Theret技术的启发下，我们用生成函数证明了Ginzburg-Gurel关于哈密顿微分同态$\mathbb{C}\text{P}^d$的周期点的最新结果。例如，我们能够证明伪旋转的不动点作为不动集是孤立的，或者具有双曲不动点的哈密顿微分同构具有无穷多个周期点。

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On periodic points of Hamiltonian diffeomorphisms of $\mathbb{C} \mathrm{P}^d$ via generating functions

Inspired by the techniques of Givental and Theret, we provide a proof with generating functions of a recent result of Ginzburg-Gurel concerning the periodic points of Hamiltonian diffeomorphisms of $\mathbb{C}\text{P}^d$. For instance, we are able to prove that fixed points of pseudo-rotations are isolated as invariant sets or that a Hamiltonian diffeomorphism with a hyperbolic fixed point has infinitely many periodic points.

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来源期刊

Journal of Symplectic Geometry 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.