Connected Sets in Global Bifurcation Theory
Connected Sets in Global Bifurcation Theory
English | 2025 | ISBN: 3031870506 | 113 Pages | PDF EPUB (True) | 9 MB
English | 2025 | ISBN: 3031870506 | 113 Pages | PDF EPUB (True) | 9 MB
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.