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Isochronous Systems

2008-02-07 Science
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Release : 2008-02-07
Genre : Science
Kind : eBook
Book Rating : 655/5 ( reviews)

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Book Synopsis Isochronous Systems by : Francesco Calogero

Download or read book Isochronous Systems written by Francesco Calogero. This book was released on 2008-02-07. Available in PDF, EPUB and Kindle. Book excerpt: A dynamical system is called isochronous if it features in its phase space an open, fully-dimensional region where all its solutions are periodic in all its degrees of freedom with the same, fixed period. Recently a simple transformation has been introduced, applicable to quite a large class of dynamical systems, that yields autonomous systems which are isochronous. This justifies the notion that isochronous systems are not rare. In this book the procedure to manufacture isochronous systems is reviewed, and many examples of such systems are provided. Examples include many-body problems characterized by Newtonian equations of motion in spaces of one or more dimensions, Hamiltonian systems, and also nonlinear evolution equations (PDEs). The book shall be of interest to students and researchers working on dynamical systems, including integrable and nonintegrable models, with a finite or infinite number of degrees of freedom. It might be used as a basic textbook, or as backup material for an undergraduate or graduate course.

The Center and Cyclicity Problems

2009-04-29 Mathematics
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Release : 2009-04-29
Genre : Mathematics
Kind : eBook
Book Rating : 279/5 ( reviews)

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Book Synopsis The Center and Cyclicity Problems by : Valery Romanovski

Download or read book The Center and Cyclicity Problems written by Valery Romanovski. This book was released on 2009-04-29. Available in PDF, EPUB and Kindle. Book excerpt: Using a computational algebra approach, this comprehensive text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The book gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. It contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography, making it a suitable graduate textbook as well as research reference.

Planar Dynamical Systems

2014-10-29 Mathematics
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Release : 2014-10-29
Genre : Mathematics
Kind : eBook
Book Rating : 142/5 ( reviews)

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Book Synopsis Planar Dynamical Systems by : Yirong Liu

Download or read book Planar Dynamical Systems written by Yirong Liu. This book was released on 2014-10-29. Available in PDF, EPUB and Kindle. Book excerpt: In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.

Notes on Hamiltonian Dynamical Systems

2022-05-05 Science
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Release : 2022-05-05
Genre : Science
Kind : eBook
Book Rating : 142/5 ( reviews)

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Book Synopsis Notes on Hamiltonian Dynamical Systems by : Antonio Giorgilli

Download or read book Notes on Hamiltonian Dynamical Systems written by Antonio Giorgilli. This book was released on 2022-05-05. Available in PDF, EPUB and Kindle. Book excerpt: Introduces Hamiltonian dynamics from the very beginning, culminating in the most important recent results: Kolmogorov's and Nekhoroshev's.

Art of Digital Audio

2013-04-26 Technology & Engineering
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Release : 2013-04-26
Genre : Technology & Engineering
Kind : eBook
Book Rating : 105/5 ( reviews)

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Book Synopsis Art of Digital Audio by : John Watkinson

Download or read book Art of Digital Audio written by John Watkinson. This book was released on 2013-04-26. Available in PDF, EPUB and Kindle. Book excerpt: Described as "the most comprehensive book on digital audio to date", it is widely acclaimed as an industry "bible". Covering the very latest developments in digital audio technology, it provides an thorough introduction to the theory as well as acting as an authoritative and comprehensive professional reference source. Everything you need is here from the fundamental principles to the latest applications, written in an award-winning style with clear explanations from first principles. New material covered includes internet audio, PC audio technology, DVD, MPEG audio compression, digital audio broadcasting and audio networks. Whether you are in the field of audio engineering, sound recording, music technology, broadcasting and communications media or audio design and installation, this book has it all. Written by a leading international audio specialist, who conducts professional seminars and workshops around the world, the book has been road tested for many years by professional seminar attendees and students to ensure their needs are taken into account, and all the right information is covered. This new edition now includes: Internet audio PC Audio technology DVD MPEG Audio compression Digital Audio Broadcasting Audio networks Digital audio professionals will find everything they need here, from the fundamental principles to the latest applications, written in an award-winning style with clear explanations from first principles. John Watkinson is an international consultant in audio, video and data recording. He is a Fellow of the AES, a member of the British Computer Society and a chartered information systems practitioner. He presents lectures, seminars, conference papers and training courses worldwide. He is the author of many other Focal Press books, including: the Kraszna-Krausz award winning MPEG-2; The Art of Digital Audio; An Introduction to Digital Video; The Art of Sound Reproduction; An Introduction to Digital Audio; TV Fundamentals and Audio for Television. He is also co-author, with Francis Rumsey, of The Digital Interface Handbook, and contributor to the Loudspeaker and Headphone Handbook, 3rd edition.

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