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The purpose of this chapter is to motivate the choice of material in the six chapters that follow. To this end it begins by reviewing classical approaches to local and global bifurcation theory, with particular attention to their conclusions about path-connectedness of bifurcating sets. It then outlines how in Chaps. 2 – 6 carefully chosen themes from point-set topology lead to further insights in global bifurcation theory, and finally it discusses how in Chap. 7 these conclusions may be illustrated by examples.

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Introduction

  • 章节

  • 发表日期：

    2025年

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  • Boris Buffoni,
  • John Toland

摘要

The purpose of this chapter is to motivate the choice of material in the six chapters that follow. To this end it begins by reviewing classical approaches to local and global bifurcation theory, with particular attention to their conclusions about path-connectedness of bifurcating sets. It then outlines how in Chaps. 2 – 6 carefully chosen themes from point-set topology lead to further insights in global bifurcation theory, and finally it discusses how in Chap. 7 these conclusions may be illustrated by examples.