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Connected Sets in Global Bifurcation Theory

Connected Sets in Global Bifurcation Theory

Paperback

Series: Springerbriefs in Mathematics

General Mathematics

ISBN10: 3031870506
ISBN13: 9783031870507
Publisher: Springer
Published: Apr 30 2025
Pages: 101
Weight: 0.38
Height: 0.24 Width: 6.14 Depth: 9.21
Language: English
This book explores the topological properties of connected and path-connected solution sets for nonlinear equations in Banach spaces, focusing on the distinction between these concepts. Building on Rabinowitz's dichotomy and classical results on Peano continua, the authors introduce congestion points--where connected sets fail to be weakly locally connected--and examine the extent to which their presence is compatible with path-connectedness. Through rigorous analysis and examples, the book provides new insights into global bifurcations.

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General Mathematics