Connected Sets in Global Bifurcation Theory
暫譯: 全球分岔理論中的連通集合

Buffoni, Boris, Toland, John

Connected Sets in Global Bifurcation Theory
  • 出版商: Springer
  • 出版日期: 2025-04-30
  • 售價: $2,430
  • 貴賓價: 9.8 折 $2,381
  • 語言: 英文
  • 頁數: 101
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031870506
  • ISBN-13: 9783031870507
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

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.

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.

商品描述(中文翻譯)

本書探討了巴拿赫空間中非線性方程的連通解集和路徑連通解集的拓撲性質，重點在於這些概念之間的區別。在拉賓諾維茨的二分法和皮亞諾連續體的經典結果的基礎上，作者引入了「擁擠點」——即連通集未能弱局部連通的地方——並檢視其存在與路徑連通性之間的相容性。通過嚴謹的分析和範例，本書提供了對全局分岔的新見解。

本書分為七章，首先介紹全局分岔理論以及集合論和度量空間的基礎概念。隨後的章節深入探討連通性、局部連通性和擁擠點，最終構建出複雜的範例，突顯解集的複雜性。作者精心選擇的材料和流暢的寫作風格使本書成為功能分析和分岔理論的博士生及專家的寶貴資源。

作者簡介

Boris Buffoni works at the Institute of Mathematics at EPFL (Ecole Polytechnique Fédérale de Lausanne, Switzerland), where he has taught since 1998. His doctorate, under the supervision of Charles Stuart at EPFL, focused on nonlinear problems in the presence of essential spectrum. He was a postdoctoral researcher at the University of Bath and the Scuola Normale Superiore in Pisa, and, from 1995 to 1998, a lecturer at the University of Bath. His research interests include calculus of variations, bifurcation theory, partial differential equations and applications to hydrodynamics. He is currently a senior scientist at EPFL.

John Toland is Emeritus Professor of Mathematics at the University of Bath where he was professor for 32 years before being appointed Director of the Isaac Newton Institute in Cambridge.

His PhD, under the supervision of Charles Stuart at Sussex University, was on global bifurcation theory for k-set-contractions after which, with collaborators, he developed topological methods to prove the existence of large amplitude solitary waves, including the famous singular Stokes-wave-of-greatest-height. Since then he has developed aspects of convex analysis, harmonic analysis, duality theory, Nash-Moser theory and variational methods, to address nonlinear problems arising in applications.

作者簡介(中文翻譯)

Boris Buffoni 目前在瑞士洛桑聯邦理工學院 (EPFL) 的數學研究所工作，自 1998 年以來一直擔任教職。他的博士學位是在 EPFL 由 Charles Stuart 指導，研究重點是存在本質頻譜的非線性問題。他曾在巴斯大學和比薩的高等師範學校擔任博士後研究員，並於 1995 年至 1998 年期間擔任巴斯大學的講師。他的研究興趣包括變分法、分岔理論、偏微分方程及其在流體力學中的應用。目前他是 EPFL 的高級科學家。

John Toland 是巴斯大學的名譽數學教授，曾在該校任教 32 年，之後被任命為劍橋的艾薩克·牛頓研究所所長。

他的博士學位是在薩塞克斯大學由 Charles Stuart 指導，研究主題為 k-集收縮的全局分岔理論，之後與合作者一起發展了拓撲方法，以證明大幅度孤立波的存在，包括著名的最大高度奇異斯托克斯波。自那時以來，他發展了凸分析、調和分析、對偶理論、Nash-Moser 理論和變分方法的各個方面，以解決應用中出現的非線性問題。

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