Poincare-Birkhoff 固定點定理之研究與探討

Abstract

本文最要是把Poincare-Birkhoff fixed point theorem的證明清楚的寫下來,因為當 初Birkoff給的證明還有一些地方不是很清楚,再加上這個定理在撞球周期軌跡問 題上一個有趣的應用。

This paper further modifies Brown and Neumann’s proof to make it as clear as possible, clarifying what the previous renditions have left unclear.Moreover, the periodic trajectories problem of billiard is chosen as a application of the Poincare-Birkhoff fixed point theorem.