Integrable Geodesic Flows On Two Dimensional Surfaces

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Integrable Geodesic Flows on Two-Dimensional Surfaces

Author : A.V. Bolsinov
Publisher : Springer
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Integrable Geodesic Flows on Two-Dimensional Surfaces by : A.V. Bolsinov

Download or read book Integrable Geodesic Flows on Two-Dimensional Surfaces written by A.V. Bolsinov and published by Springer. This book was released on 2000 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Moscow State University, Bolsinov (computer methods) and Fomenko (differential geometry) present a new approach to the qualitative analysis of the particular type of geodesic flow of Riemannian metrics on manifolds based on the theory of topological classification of integrable Hamiltonian systems. They begin by introducing the qualitative theory of integrable Hamiltonian systems, then discuss the class of integrable geodesic flows on two-dimensional surfaces from both the classical and contemporary perspectives. They classify the flows according to equivalence relations, such as isometry, the Liouville equivalence, the smooth and continuous trajectory equivalence, and the geodesic equivalence. They also explain the new technique that makes such classification possible. Many of their results have not been published before. The Russian original is Geometriia i topologiia integriruemykh geodezicheskikh potokov na poverkhnostiakhAnnotation copyrighted by Book News, Inc., Portland, OR

Integrable Hamiltonian Systems

Author : A.V. Bolsinov
Publisher : CRC Press
ISBN 13 : 0203643429
Total Pages : 752 pages
Book Rating : 4.2/5 (36 download)

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Book Synopsis Integrable Hamiltonian Systems by : A.V. Bolsinov

Download or read book Integrable Hamiltonian Systems written by A.V. Bolsinov and published by CRC Press. This book was released on 2004-02-25 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,

Integrable Geodesic Flows on Two-Dimensional Surfaces

Author : A.V. Bolsinov
Publisher : Springer
ISBN 13 : 9781461543077
Total Pages : 0 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Integrable Geodesic Flows on Two-Dimensional Surfaces by : A.V. Bolsinov

Download or read book Integrable Geodesic Flows on Two-Dimensional Surfaces written by A.V. Bolsinov and published by Springer. This book was released on 2013-05-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geodesic flows of Riemannian metrics on manifolds are one of the classical objects in geometry. A particular place among them is occupied by integrable geodesic flows. We consider them in the context of the general theory of integrable Hamiltonian systems, and in particular, from the viewpoint of a new topological classification theory, which was recently developed for integrable Hamiltonian systems with two degrees of freedom. As a result, we will see that such a new approach is very useful for a deeper understanding of the topology and geometry of integrable geodesic flows. The main object to be studied in our paper is the class of integrable geodesic flows on two-dimensional surfaces. There are many such flows on surfaces of small genus, in particular, on the sphere and torus. On the contrary, on surfaces of genus 9 > 1, no such flows exist in the analytical case. One of the most important and interesting problems consists in the classification of integrable flows up to different equivalence relations such as (1) an isometry, (2) the Liouville equivalence, (3) the trajectory equivalence (smooth and continuous), and (4) the geodesic equivalence. In recent years, a new technique was developed, which gives, in particular, a possibility to classify integrable geodesic flows up to these kinds of equivalences. This technique is presented in our paper, together with various applications. The first part of our book, namely, Chaps.

Symplectic Geometry

Author : A.T. Fomenko
Publisher : CRC Press
ISBN 13 : 9782881249013
Total Pages : 488 pages
Book Rating : 4.2/5 (49 download)

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Book Synopsis Symplectic Geometry by : A.T. Fomenko

Download or read book Symplectic Geometry written by A.T. Fomenko and published by CRC Press. This book was released on 1995-11-30 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Integrability and Nonintegrability in Geometry and Mechanics

Author : A.T. Fomenko
Publisher : Springer Science & Business Media
ISBN 13 : 9400930690
Total Pages : 358 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Integrability and Nonintegrability in Geometry and Mechanics by : A.T. Fomenko

Download or read book Integrability and Nonintegrability in Geometry and Mechanics written by A.T. Fomenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. 1hen one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin' . • 1111 Oulik'. n. . Chi" •. • ~ Mm~ Mu,d. ", Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Proceedings of the Workshop Contemporary Geometry and Related Topics

Author : Neda Bokan
Publisher : World Scientific
ISBN 13 : 9812384324
Total Pages : 469 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Proceedings of the Workshop Contemporary Geometry and Related Topics by : Neda Bokan

Download or read book Proceedings of the Workshop Contemporary Geometry and Related Topics written by Neda Bokan and published by World Scientific. This book was released on 2004 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readership: Researchers in geometry & topology, nonlinear science and dynamical systems.

Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable

Author : Kazuyoshi Kiyohara
Publisher : American Mathematical Soc.
ISBN 13 : 0821806408
Total Pages : 159 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable by : Kazuyoshi Kiyohara

Download or read book Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable written by Kazuyoshi Kiyohara and published by American Mathematical Soc.. This book was released on 1997 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.

Topological Classification of Integrable Systems

Author : A. T. Fomenko
Publisher : American Mathematical Soc.
ISBN 13 : 9780821841051
Total Pages : 448 pages
Book Rating : 4.8/5 (41 download)

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Book Synopsis Topological Classification of Integrable Systems by : A. T. Fomenko

Download or read book Topological Classification of Integrable Systems written by A. T. Fomenko and published by American Mathematical Soc.. This book was released on 1991 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modern Mathematics and Mechanics

Author : Victor A. Sadovnichiy
Publisher : Springer
ISBN 13 : 331996755X
Total Pages : 564 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Modern Mathematics and Mechanics by : Victor A. Sadovnichiy

Download or read book Modern Mathematics and Mechanics written by Victor A. Sadovnichiy and published by Springer. This book was released on 2018-11-29 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems. These abstract mathematical approaches are applied to problem-solving in solid mechanics, hydro- and aerodynamics, optimization, decision making theory and control theory. This volume is therefore relevant to mathematicians as well as engineers working at the interface of these fields.

Continuous and Distributed Systems II

Author : Viktor A. Sadovnichiy
Publisher : Springer
ISBN 13 : 331919075X
Total Pages : 395 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Continuous and Distributed Systems II by : Viktor A. Sadovnichiy

Download or read book Continuous and Distributed Systems II written by Viktor A. Sadovnichiy and published by Springer. This book was released on 2015-06-04 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: As in the previous volume on the topic, the authors close the gap between abstract mathematical approaches, such as applied methods of modern algebra and analysis, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems, on the one hand and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in biochemistry, geophysics, biology and climatology. This compilation will be of interest to mathematicians and engineers working at the interface of these fields. It presents selected works of the joint seminar series of Lomonosov Moscow State University and the Institute for Applied System Analysis at National Technical University of Ukraine “Kyiv Polytechnic Institute”. The authors come from Brazil, Germany, France, Mexico, Spain, Poland, Russia, Ukraine and the USA.

Interrelationship Among Aging, Cancer and Differentiation

Author : Bernard Pullman
Publisher : Springer Science & Business Media
ISBN 13 : 9789027721174
Total Pages : 732 pages
Book Rating : 4.7/5 (211 download)

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Book Synopsis Interrelationship Among Aging, Cancer and Differentiation by : Bernard Pullman

Download or read book Interrelationship Among Aging, Cancer and Differentiation written by Bernard Pullman and published by Springer Science & Business Media. This book was released on 1985-11-30 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Eighteenth Jerusalem Symposium on Quantum Chemistry and Biochemistry held in Jerusalem, Israel, April 29-May 2, 1985

Advances in Dynamical Systems and Control

Author : Victor A. Sadovnichiy
Publisher : Springer
ISBN 13 : 3319406736
Total Pages : 477 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Advances in Dynamical Systems and Control by : Victor A. Sadovnichiy

Download or read book Advances in Dynamical Systems and Control written by Victor A. Sadovnichiy and published by Springer. This book was released on 2016-08-16 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.

Contemporary Geometry And Related Topics, Proceedings Of The Workshop

Author : Neda Bokan
Publisher : World Scientific
ISBN 13 : 981448556X
Total Pages : 469 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Contemporary Geometry And Related Topics, Proceedings Of The Workshop by : Neda Bokan

Download or read book Contemporary Geometry And Related Topics, Proceedings Of The Workshop written by Neda Bokan and published by World Scientific. This book was released on 2004-03-15 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers a broad range of subjects in modern geometry and related branches of mathematics, physics and computer science. Most of the papers show new, interesting results in Riemannian geometry, homotopy theory, theory of Lie groups and Lie algebras, topological analysis, integrable systems, quantum groups, and noncommutative geometry. There are also papers giving overviews of the recent achievements in some special topics, such as the Willmore conjecture, geodesic mappings, Weyl's tube formula, and integrable geodesic flows. This book provides a great chance for interchanging new results and ideas in multidisciplinary studies.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

Partial Differential Equations I

Author : Michael E. Taylor
Publisher : Springer Nature
ISBN 13 : 3031338596
Total Pages : 734 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Partial Differential Equations I by : Michael E. Taylor

Download or read book Partial Differential Equations I written by Michael E. Taylor and published by Springer Nature. This book was released on 2023-12-06 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. In includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998)

Differential Geometry and Integrable Systems

Author : Martin A. Guest
Publisher : American Mathematical Soc.
ISBN 13 : 0821829386
Total Pages : 370 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Differential Geometry and Integrable Systems by : Martin A. Guest

Download or read book Differential Geometry and Integrable Systems written by Martin A. Guest and published by American Mathematical Soc.. This book was released on 2002 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced byintegrable systems. This book is the first of three collections of expository and research articles. This volume focuses on differential geometry. It is remarkable that many classical objects in surface theory and submanifold theory are described as integrable systems. Having such a description generallyreveals previously unnoticed symmetries and can lead to surprisingly explicit solutions. Surfaces of constant curvature in Euclidean space, harmonic maps from surfaces to symmetric spaces, and analogous structures on higher-dimensional manifolds are some of the examples that have broadened the horizons of differential geometry, bringing a rich supply of concrete examples into the theory of integrable systems. Many of the articles in this volume are written by prominent researchers and willserve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The second volume from this conference also available from the AMS is Integrable Systems,Topology, and Physics, Volume 309 CONM/309in the Contemporary Mathematics series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the AMS in the Advanced Studies in Pure Mathematics series.

Geometric Methods in Physics XXXV

Author : Piotr Kielanowski
Publisher : Birkhäuser
ISBN 13 : 3319635948
Total Pages : 280 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Geometric Methods in Physics XXXV by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXV written by Piotr Kielanowski and published by Birkhäuser. This book was released on 2018-02-10 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.

Partial Differential Equations

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 9780387946542
Total Pages : 590 pages
Book Rating : 4.9/5 (465 download)

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Book Synopsis Partial Differential Equations by : Michael E. Taylor

Download or read book Partial Differential Equations written by Michael E. Taylor and published by Springer Science & Business Media. This book was released on 1996-06-25 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Companion texts, which take the theory of partial differential equations further, are AMS volume 116, treating more advanced topics in linear PDE, and AMS volume 117, treating problems in nonlinear PDE. This book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.