HANDEL'S FIXED POINT THEOREM:A MORSE THEORETICAL POINT OF VIEW  

作　　者：Patrice LE CALVEZ 

机构地区：[1]Institut de Mathématiques de Jussieu-Paris Rive Gauche,IMJ-PRG,Sorbonne Université,UniversitéParis-Diderot,CNRS,F-75005,Paris,France [2]Institut Universitaire de France,Paris,France

出　　处：《Acta Mathematica Scientia》2021年第6期2149-2172,共24页数学物理学报（B辑英文版）

摘　　要：Michael Handel has proved in [10] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that turned out to be an efficient tool in the study of the dynamics of surface homeomorphisms. The present article fits into a series of articles by the author [13] and by Juliana Xavier [21, 22], where proofs were given, related to the classical Brouwer Theory, instead of the Homotopical Brouwer Theory used in the original article. Like in [13, 21] and [22], we will use “free brick decompositions” but will present a more conceptual Morse theoretical argument. It is based on a new preliminary lemma, that gives a nice “condition at infinity” for our problem.

关 键 词：brick decomposition Brouwer theory translation arc 

分 类 号：O177.91[理学—数学]