Normal Forms, Bifurcations and Finiteness Problems in Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Normal Forms, Bifurcations and Finiteness Problems in Differential Equations write by Christiane Rousseau. This book was released on 2004-02-29. Normal Forms, Bifurcations and Finiteness Problems in Differential Equations available in PDF, EPUB and Kindle. Proceedings of the Nato Advanced Study Institute, held in Montreal, Canada, from 8 to 19 July 2002
Normal Forms, Bifurcations and Finiteness Problems in Differential Equations
Normal Forms, Bifurcations and Finiteness Problems in Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Normal Forms, Bifurcations and Finiteness Problems in Differential Equations write by Yulij Ilyashenko. This book was released on 2004-03-14. Normal Forms, Bifurcations and Finiteness Problems in Differential Equations available in PDF, EPUB and Kindle. A number of recent significant developments in the theory of differential equations are presented in an elementary fashion, many of which are scattered throughout the literature and have not previously appeared in book form, the common denominator being the theory of planar vector fields (real or complex). A second common feature is the study of bifurcations of dynamical systems. Moreover, the book links fields that have developed independently and signposts problems that are likely to become significant in the future. The following subjects are covered: new tools for local and global properties of systems and families of systems, nonlocal bifurcations, finiteness properties of Pfaffian functions and of differential equations, geometric interpretation of the Stokes phenomena, analytic theory of ordinary differential equations and complex foliations, applications to Hilbert's 16th problem.
Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles
Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles write by Maoan Han. This book was released on 2012-04-23. Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles available in PDF, EPUB and Kindle. 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.
Geometric Configurations of Singularities of Planar Polynomial Differential Systems
Geometric Configurations of Singularities of Planar Polynomial Differential Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Configurations of Singularities of Planar Polynomial Differential Systems write by Joan C. Artés. This book was released on 2021-07-19. Geometric Configurations of Singularities of Planar Polynomial Differential Systems available in PDF, EPUB and Kindle. This book addresses the global study of finite and infinite singularities of planar polynomial differential systems, with special emphasis on quadratic systems. While results covering the degenerate cases of singularities of quadratic systems have been published elsewhere, the proofs for the remaining harder cases were lengthier. This book covers all cases, with half of the content focusing on the last non-degenerate ones. The book contains the complete bifurcation diagram, in the 12-parameter space, of global geometrical configurations of singularities of quadratic systems. The authors’ results provide - for the first time - global information on all singularities of quadratic systems in invariant form and their bifurcations. In addition, a link to a very helpful software package is included. With the help of this software, the study of the algebraic bifurcations becomes much more efficient and less time-consuming. Given its scope, the book will appeal to specialists on polynomial differential systems, pure and applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph.D. students, and postdoctoral fellows.
On Finiteness in Differential Equations and Diophantine Geometry
On Finiteness in Differential Equations and Diophantine Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Finiteness in Differential Equations and Diophantine Geometry write by Dana Schlomiuk. This book was released on . On Finiteness in Differential Equations and Diophantine Geometry available in PDF, EPUB and Kindle. This book focuses on finiteness conjectures and results in ordinary differential equations (ODEs) and Diophantine geometry. During the past twenty-five years, much progress has been achieved on finiteness conjectures, which are the offspring of the second part of Hilbert's 16th problem. Even in its simplest case, this is one of the very few problems on Hilbert's list which remains unsolved. These results are about existence and estimation of finite bounds for the number of limit cycles occurring in certain families of ODEs. The book describes this progress, the methods used (bifurcation theory, asymptotic expansions, methods of differential algebra, or geometry) and the specific results obtained. The finiteness conjectures on limit cycles are part of a larger picture that also includes finiteness problems in other areas of mathematics, in particular those in Diophantine geometry where remarkable results were proved during the same period of time. There is a chapter devoted to finiteness results in D The volume can be used as an independent study text for advanced undergraduates and graduate students studying ODEs or applications of differential algebra to differential equations and Diophantine geometry. It is also is a good entry point for researchers interested these areas, in particular, in limit cycles of ODEs, and in finiteness problems. Contributors to the volume include Andrey Bolibrukh and Alexandru Buium. Available from the AMS by A. Buium is Arithmetic Differential Equations, as Volume 118 in the Mathematical Surveys and Monographs series.
