An Introduction to Dynamical Systems and Chaos

Layek, G. C.

An Introduction to Dynamical Systems and Chaos
  • 出版商: Springer
  • 出版日期: 2024-02-24
  • 售價: $3,660
  • 貴賓價: 9.5 折 $3,477
  • 語言: 英文
  • 頁數: 688
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 9819976944
  • ISBN-13: 9789819976942

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相關主題

商品描述

This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable coexisting attractors. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, featuring a multitude of detailed worked-out examples alongside comprehensive exercises. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate, graduate and research students in mathematics, physics and engineering.

The second edition of the book is thoroughly revised and includes several new topics: center manifold reduction, quasi-periodic oscillations, Bogdanov-Takens, periodbubbling and Neimark-Sacker bifurcations, and dynamics on circle. The organized structures in bi-parameter plane for transitional and chaotic regimes are new active research interest and explored thoroughly. The connections of complex chaotic attractors with fractals cascades are explored in many physical systems. Chaotic attractors may attain multiple scaling factors and show scale invariance property. Finally, the ideas of multifractals and global spectrum for quantifying inhomogeneous chaotic attractors are discussed.

商品描述(中文翻譯)

本書系統且有序地討論連續和離散的非線性系統。該書的獨特之處在於其對流動分叉、非線性振動、非線性系統的Lie對稱分析、混沌理論、混沌路徑和多穩定共存吸引子的數學理論。邏輯結構的內容和順序導向為讀者提供了對該主題的整體概述。採用了系統的數學方法，並提供了大量詳細的實例和全面的練習題。本書適用於高級本科生、研究生和數學、物理和工程學研究生的動力系統、混沌和非線性動力學課程。

該書的第二版經過全面修訂，並包括幾個新主題：中心流形簡化、準周期振動、Bogdanov-Takens、周期泡沫和Neimark-Sacker分叉，以及圓上的動力學。過渡和混沌區域的雙參數平面中的有組織結構是新的研究興趣，並得到了徹底的探索。在許多物理系統中，探索了複雜混沌吸引子與分形級聯之間的聯繫。混沌吸引子可能具有多個尺度因子並展示尺度不變性。最後，討論了多重分形和全局頻譜的概念，以量化不均勻混沌吸引子。

作者簡介

G. C. LAYEK is a Professor of the Department of Mathematics, The University of Burdwan, India. He received his Ph.D. degree from Indian Institute of Technology, Kharagpur and did his Post doctoral studies at Indian Statistical Institute, Kolkata. His areas of research are nonlinear dynamics, chaos theory, turbulence, boundary layer flows and thermal sciences. Professor Layek has published more than 100 research papers in international journals of repute. He taught more than two decades at the post-graduate level in the University of Burdwan. He made several international academic visits, such asLaboratoire de Me ́canique des Fluides de Lille (LMFL), Centrale Lille, France as 'Professeur invitaé', Saint Petersburg State University and Kazan State Technological University, Russia for collaborative research works. Layek and Pati's model (Physics Letters A, 381: 3568-3575, 2017) got recognition for exploring bifurcations and Shil'nikov chaos in Rayleigh-Bénard convection of a Boussinesq fluid layer heated underneath taking non-Fourier heat-flux. The existence of non-Kolmogorov turbulence is established for free-shear turbulent flows, viz., turbulent wake, jet and thermal plume flows through Lie symmetry analysis on statistical turbulent model equations. He has made significant contributions for identification of organized structures in transitional routes and chaotic regimes of many physical phenomena.He now focuses research works on organized structures in chaos and turbulence.

作者簡介(中文翻譯)

G. C. LAYEK是印度Burdwan大學數學系的教授。他在印度理工學院Kharagpur獲得博士學位，並在印度統計學研究所Kolkata進行博士後研究。他的研究領域包括非線性動力學、混沌理論、湍流、邊界層流和熱科學。Layek教授在國際知名期刊上發表了100多篇研究論文。他在Burdwan大學的研究生課程中教授了二十多年。他曾多次進行國際學術訪問，例如作為“Professeur invitaé”在法國里爾的里爾流體力學實驗室（LMFL）和里爾中央學院，以及在俄羅斯的聖彼得堡國立大學和喀山國立技術大學進行合作研究。Layek和Pati的模型（Physics Letters A, 381: 3568-3575, 2017）因探索Boussinesq流體層底部加熱的Rayleigh-Bénard對流中的分歧和Shil'nikov混沌而獲得認可，該模型考慮了非傅立葉熱通量。通過對統計湍流模型方程的Lie對稱性分析，確定了自由剪切湍流流動（如湍流尾流、射流和熱柱流動）中存在非Kolmogorov湍流。他在許多物理現象的過渡路徑和混沌區域中識別有組織結構方面做出了重要貢獻。他現在專注於混沌和湍流中的有組織結構的研究工作。

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