國立虎尾科技大學 |

Connected sets in global bifurcation theory

Record Type:	Language materials, printed : 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.;
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:

527837
Bifurcation theory.

LC Class. No.: QA380

Dewey Class. No.: 515.35

Connected sets in global bifurcation theory
LDR:02215nam a2200337 a 4500 001 1162500
003 DE-He213
005 20250429130209.0
006 m d
007 cr nn 008maaau
008 251029s2025 sz s 0 eng d
020 $a 9783031870514 $q (electronic bk.)
020 $a 9783031870507 $q (paper)
024 7 $a 10.1007/978-3-031-87051-4 $2 doi
035 $a 978-3-031-87051-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA380
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.35 $2 23
090 $a QA380 $b .B929 2025
100 1 $a Buffoni, Boris. $3 1489297
245 1 0 $a Connected sets in global bifurcation theory $h [electronic resource] / $c by Boris Buffoni, John Toland.
260 $a Cham : $c 2025. $b Springer Nature Switzerland : $b Imprint: Springer,
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 527837
650 1 4 $a Functional Analysis. $3 672166
650 2 4 $a Topology. $3 633483
650 2 4 $a Differential Equations. $3 681826
650 2 4 $a Dynamical Systems. $3 1366074
700 1 $a Toland, John. $e author. $3 1313877
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs in mathematics. $3 883715
856 4 0 $u https://doi.org/10.1007/978-3-031-87051-4
950 $a Mathematics and Statistics (SpringerNature-11649)