A symplectic proof of a theorem of Franks

被引：18

作者：

Collier, Brian ^{[1
]}

Kerman, Ely ^{[1
]}

Reiniger, Benjamin M. ^{[1
]}

Turmunkh, Bolor ^{[1
]}

Zimmer, Andrew ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

COMPOSITIO MATHEMATICA | 2012年 / 148卷 / 06期

基金：

美国国家科学基金会;

关键词：

periodic orbits; Hamiltonian flows; Floer homology; FLOER HOMOLOGY; PERIODIC-SOLUTIONS; MORSE-THEORY; ORBITS; POINTS;

D O I：

10.1112/S0010437X12000474

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A celebrated theorem in two-dimensional dynamics due to John Franks asserts that every area-preserving homeomorphism of the sphere has either two or infinitely many periodic points. In this work we re-prove Franks' theorem under the additional assumption that the map is smooth. Our proof uses only tools from symplectic topology and thus differs significantly from previous proofs. A crucial role is played by the results of Ginzburg and Kerman concerning resonance relations for Hamiltonian diffeomorphisms.

引用

页码：1969 / 1984

页数：16

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[2]

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[4]

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