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Author: H.W Broer
Publisher: CRC Press
ISBN: 9781420034288
Category : Mathematics
Languages : en
Pages : 498
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Book Description
Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.
Author: H.W Broer
Publisher: CRC Press
ISBN: 9781420034288
Category : Mathematics
Languages : en
Pages : 498
Get Book Here
Book Description
Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.
Author: Michael Shub
Publisher: Springer
ISBN: 9781441930798
Category : Mathematics
Languages : en
Pages : 150
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Book Description
These notes are the result of a course in dynamical systems given at Orsay during the 1976-77 academic year. I had given a similar course at the Gradu ate Center of the City University of New York the previous year and came to France equipped with the class notes of two of my students there, Carol Hurwitz and Michael Maller. My goal was to present Smale's n-Stability Theorem as completely and compactly as possible and in such a way that the students would have easy access to the literature. I was not confident that I could do all this in lectures in French, so I decided to distribute lecture notes. I wrote these notes in English and Remi Langevin translated them into French. His work involved much more than translation. He consistently corrected for style, clarity, and accuracy. Albert Fathi got involved in reading the manuscript. His role quickly expanded to extensive rewriting and writing. Fathi wrote (5. 1) and (5. 2) and rewrote Theorem 7. 8 when I was in despair of ever getting it right with all the details. He kept me honest at all points and played a large role in the final form of the manuscript. He also did the main work in getting the manuscript ready when I had left France and Langevin was unfortunately unavailable. I ran out of steam by the time it came to Chapter 10. M.
Author: Donald W. Kahn
Publisher: Courier Corporation
ISBN: 0486152294
Category : Mathematics
Languages : en
Pages : 20
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Book Description
This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.
Author: Jian-Qiao Sun
Publisher: Springer Science & Business Media
ISBN: 146143128X
Category : Technology & Engineering
Languages : en
Pages : 297
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Book Description
Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time.
Author: Achintya Haldar
Publisher: World Scientific
ISBN: 9810231288
Category : Technology & Engineering
Languages : en
Pages : 437
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Book Description
The functionality of modern structural, mechanical and electrical or electronic systems depends on their ability to perform under uncertain conditions. Consideration of uncertainties and their effect on system behavior is an essential and integral part of defining systems. In eleven chapters, leading experts present an overview of the current state of uncertainty modeling, analysis and design of large systems in four major areas: finite and boundary element methods (common structural analysis techniques), fatigue, stability analysis, and fault-tolerant systems. The content of this book is unique; it describes exciting research developments and challenges in emerging areas, and provide a sophisticated toolbox for tackling uncertainty modeling in real systems.
Author: Mohd Hafiz Mohd
Publisher: Springer Nature
ISBN: 9813298324
Category : Mathematics
Languages : en
Pages : 239
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Book Description
This book is the result of ​Southeast Asian Mathematical Society (SEAMS) School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA). It addresses the latest developments in the field of dynamical systems, and highlights the importance of numerical continuation studies in tracking both stable and unstable steady states and bifurcation points to gain better understanding of the dynamics of the systems. The SEAMS School 2018 on DySBA was held in Penang from 6th to 13th August at the School of Mathematical Sciences, Universiti Sains Malaysia.The SEAMS Schools are part of series of intensive study programs that aim to provide opportunities for an advanced learning experience in mathematics via planned lectures, contributed talks, and hands-on workshop. This book will appeal to those postgraduates, lecturers and researchers working in the field of dynamical systems and their applications. Senior undergraduates in Mathematics will also find it useful.
Author: Jerrold E. Marsden
Publisher:
ISBN:
Category : Global analysis (Mathematics)
Languages : en
Pages : 292
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Book Description
Author: Andrew Stuart
Publisher: Cambridge University Press
ISBN: 9780521645638
Category : Mathematics
Languages : en
Pages : 708
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Book Description
The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 0821841432
Category : Mathematics
Languages : en
Pages : 394
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Book Description
"Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".
Author: B. Fiedler
Publisher: Gulf Professional Publishing
ISBN: 0080532845
Category : Science
Languages : en
Pages : 1099
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Book Description
This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.
