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Connected sets in global bifurcation theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Connected sets in global bifurcation theory/ by Boris Buffoni, John Toland.
Author:	Buffoni, Boris.
other author:	Toland, John.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xii, 101 p. :ill., digital ;24 cm.
[NT 15003449]:	- 1. Introduction -- 2. Set Theory Foundations -- 3. Metric Spaces -- 4. Types of Connectedness -- 5. Congestion Points -- 6. Decomposable and Indecomposable Continua -- 7. Pathological Examples.
Contained By:	Springer Nature eBook
Subject:	Bifurcation theory. -
Online resource:	https://doi.org/10.1007/978-3-031-87051-4
ISBN:	9783031870514

Connected sets in global bifurcation theory
Buffoni, Boris.

Connected sets in global bifurcation theory[electronic resource] /by Boris Buffoni, John Toland. - Cham :Springer Nature Switzerland :2025. - xii, 101 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

- 1. Introduction -- 2. Set Theory Foundations -- 3. Metric Spaces -- 4. Types of Connectedness -- 5. Congestion Points -- 6. Decomposable and Indecomposable Continua -- 7. Pathological Examples.

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, the authors introduce "congestion points"-where connected sets fail to be locally connected-and show their absence ensures path-connectedness. Through rigorous analysis and examples, the book provides new insights into global bifurcations. Structured into seven chapters, the book begins with an introduction to global bifurcation theory and foundational concepts in set theory and metric spaces. Subsequent chapters delve into connectedness, local connectedness, and congestion points, culminating in the construction of intricate examples that highlight the complexities of solution sets. The authors' careful selection of material and fluent writing style make this work a valuable resource for PhD students and experts in functional analysis and bifurcation theory.

ISBN: 9783031870514

Standard No.: 10.1007/978-3-031-87051-4doiSubjects--Topical Terms:

544229
Bifurcation theory.

LC Class. No.: QA380

Dewey Class. No.: 515.35

Connected sets in global bifurcation theory
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245 1 0 $a Connected sets in global bifurcation theory $h [electronic resource] / $c by Boris Buffoni, John Toland.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xii, 101 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8201
505 0 $a - 1. Introduction -- 2. Set Theory Foundations -- 3. Metric Spaces -- 4. Types of Connectedness -- 5. Congestion Points -- 6. Decomposable and Indecomposable Continua -- 7. Pathological Examples.
520 $a 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, the authors introduce "congestion points"-where connected sets fail to be locally connected-and show their absence ensures path-connectedness. Through rigorous analysis and examples, the book provides new insights into global bifurcations. Structured into seven chapters, the book begins with an introduction to global bifurcation theory and foundational concepts in set theory and metric spaces. Subsequent chapters delve into connectedness, local connectedness, and congestion points, culminating in the construction of intricate examples that highlight the complexities of solution sets. The authors' careful selection of material and fluent writing style make this work a valuable resource for PhD students and experts in functional analysis and bifurcation theory.
650 0 $a Bifurcation theory. $3 544229
650 1 4 $a Functional Analysis. $3 893943
650 2 4 $a Topology. $3 522026
650 2 4 $a Differential Equations. $3 907890
650 2 4 $a Dynamical Systems. $3 3538746
700 1 $a Toland, John. $3 3530387
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950 $a Mathematics and Statistics (SpringerNature-11649)