Download or read book Normal Forms and Homoclinic Chaos written by William F. Langford and published by American Mathematical Soc.. This book was released on 1995-01-01 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents new research on normal forms, symmetry, homoclinic cycles, and chaos, from the Workshop on Normal Forms and Homoclinic Chaos held during The Fields Institute Program Year on Dynamical Systems and Bifurcation Theory in November 1992, in Waterloo, Canada. The workshop bridged the local and global analysis of dynamical systems with emphasis on normal forms and the recently discovered homoclinic cycles which may arise in normal forms. Specific topics covered in this volume include normal forms for dissipative, conservative, and reversible vector fields, and for symplectic maps; the effects of symmetry on normal forms; the persistence of homoclinic cycles; symmetry-breaking, both spontaneous and induced; mode interactions; resonances; intermittency; numerical computation of orbits in phase space; applications to flow-induced vibrations and to mechanical and structural systems; general methods for calculation of normal forms; and chaotic dynamics arising from normal forms. Of the 32 presentations given at this workshop, 14 of them are represented by papers in this volume.
Download or read book The Method of Normal Forms written by Ali H. Nayfeh and published by John Wiley & Sons. This book was released on 2011-08-29 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this introductory treatment Ali Nayfeh presents different concepts from dynamical systems theory and nonlinear dynamics in a rigorous yet plan way. He systematically introduces models and techniques and states the relevant ranges of validity and applicability. The reader is provided with a clear operational framework for consciously use rather than focused on the underlying mathematical apparatus. The exposition is largely by means of examples, dealt with up to their final outcome. For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging. The previous edition had a remarkable success by researchers from all over the world working in the area of nonlinear dynamics and their applications in engineering. Additions to this new edition concern major topics of current interest. In particular, the author added three new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems. In particular the latter has become of major importance in several applications, both in mechanics and in different areas. Accessible to engineers and applied scientist involved with nonlinear dynamics and their applications in a wide variety of fields. It is assumed that readers have a knowledge of basic calculus as well as the elementary properties of ordinary-differential equations.
Download or read book Smooth Invariant Manifolds And Normal Forms written by Alexander Kopanskii and published by World Scientific. This book was released on 1994-12-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the qualitative theory of dynamical systems and is devoted to the study of flows and cascades in the vicinity of a smooth invariant manifold. Its main purpose is to present, as completely as possible, the basic results concerning the existence of stable and unstable local manifolds and the recent advancements in the theory of finitely smooth normal forms of vector fields and diffeomorphisms in the vicinity of a rest point and a periodic trajectory. A summary of the results obtained so far in the investigation of dynamical systems near an arbitrary invariant submanifold is also given.
Download or read book Normal Forms Melnikov Functions and Bifurcations of Limit Cycles written by Maoan Han and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.
Download or read book Poisson Structures and Their Normal Forms written by Jean-Paul Dufour and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.
Download or read book Normal Forms and Unfoldings for Local Dynamical Systems written by James Murdock and published by Springer Science & Business Media. This book was released on 2006-04-10 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the most thorough treatment of normal forms currently existing in book form. There is a substantial gap between elementary treatments in textbooks and advanced research papers on normal forms. This book develops all the necessary theory 'from scratch' in just the form that is needed for the application to normal forms, with as little unnecessary terminology as possible.
Download or read book Normal Forms and Stability of Hamiltonian Systems written by Hildeberto E. Cabral and published by Springer Nature. This book was released on 2023-09-12 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics. This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems. With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.
Download or read book Normal Forms Bifurcations and Finiteness Problems in Differential Equations written by Christiane Rousseau and published by Springer Science & Business Media. This book was released on 2004-02-29 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Nato Advanced Study Institute, held in Montreal, Canada, from 8 to 19 July 2002
Download or read book Local Bifurcations Center Manifolds and Normal Forms in Infinite Dimensional Dynamical Systems written by Mariana Haragus and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
Download or read book Grobner shirshov Bases Normal Forms Combinatorial And Decision Problems In Algebra written by Leonid Bokut and published by World Scientific. This book was released on 2020-06-16 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac-Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple Lie algebra theory, the plactic monoid theory. One of the main problems for such presentations is the problem of normal forms of their elements. Classical examples of such normal forms give the Poincaré-Birkhoff-Witt theorem for universal enveloping algebras and Artin-Markov normal form theorem for braid groups in Burau generators.What is now called Gröbner-Shirshov bases theory is a general approach to the problem. It was created by a Russian mathematician A I Shirshov (1921-1981) for Lie algebras (explicitly) and associative algebras (implicitly) in 1962. A few years later, H Hironaka created a theory of standard bases for topological commutative algebra and B Buchberger initiated this kind of theory for commutative algebras, the Gröbner basis theory. The Shirshov paper was largely unknown outside Russia. The book covers this gap in the modern mathematical literature. Now Gröbner-Shirshov bases method has many applications both for classical algebraic structures (associative, Lie algebra, groups, semigroups) and new structures (dialgebra, pre-Lie algebra, Rota-Baxter algebra, operads). This is a general and powerful method in algebra.
Download or read book The Chemical Trade Journal and Oil Paint and Colour Review written by and published by . This book was released on 1894 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Journal of Diseases of Children written by and published by . This book was released on 1919 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book International Journal of Orthodontia written by and published by . This book was released on 1915 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The American Food Journal written by and published by . This book was released on 1921 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Coccidae of Ceylon written by Edward Ernest Green and published by . This book was released on 1896 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sugar written by and published by . This book was released on 1923 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes a section in Spanish.
Download or read book Ray Tracing and Beyond written by E. R. Tracy and published by Cambridge University Press. This book was released on 2014-02-27 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This complete introduction to the use of modern ray tracing techniques in plasma physics describes the powerful mathematical methods generally applicable to vector wave equations in non-uniform media, and clearly demonstrates the application of these methods to simplify and solve important problems in plasma wave theory. Key analytical concepts are carefully introduced as needed, encouraging the development of a visual intuition for the underlying methodology, with more advanced mathematical concepts succinctly explained in the appendices, and supporting Matlab and Raycon code available online. Covering variational principles, covariant formulations, caustics, tunnelling, mode conversion, weak dissipation, wave emission from coherent sources, incoherent wave fields, and collective wave absorption and emission, all within an accessible framework using standard plasma physics notation, this is an invaluable resource for graduate students and researchers in plasma physics.
