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 2005. 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.
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.
Handbook of Geometry and Topology of Singularities V: Foliations
Handbook of Geometry and Topology of Singularities V: Foliations - 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 Handbook of Geometry and Topology of Singularities V: Foliations write by Felipe Cano. This book was released on . Handbook of Geometry and Topology of Singularities V: Foliations available in PDF, EPUB and Kindle.
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.
Geometry in Partial Differential Equations
Geometry in Partial 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 Geometry in Partial Differential Equations write by Agostino Prastaro. This book was released on 1994. Geometry in Partial Differential Equations available in PDF, EPUB and Kindle. This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
