Download or read book Integrable Systems and Riemann Surfaces of Infinite Genus written by Martin Ulrich Schmidt and published by American Mathematical Soc.. This book was released on 1996 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir develops the spectral theory of the Lax operators of nonlinear Schrödinger-like partial differential equations with periodic boundary conditions. Their special curves, i.e., the common spectrum with the periodic shifts, are generically Riemann surfaces of infinite genus. The points corresponding to infinite energy are added. The resulting spaces are no longer Riemann surfaces in the usual sense, but they are quite similar to compact Riemann surfaces.
Download or read book Riemann Surfaces of Infinite Genus written by Joel S. Feldman and published by American Mathematical Soc.. This book was released on 2003 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors geometrically construct Riemann surfaces of infinite genus by pasting together plane domains and handles. To achieve a meaningful generalization of the classical theory of Riemann surfaces to the case of infinite genus, one must impose restrictions on the asymptotic behavior of the Riemann surface. In the construction carried out here, these restrictions are formulated in terms of the sizes and locations of the handles and in terms of the gluing maps. The approach used has two main attractions. The first is that much of the classical theory of Riemann surfaces, including the Torelli theorem, can be generalized to this class. The second is that solutions of Kadomcev-Petviashvilli equations can be expressed in terms of theta functions associated with Riemann surfaces of infinite genus constructed in the book. Both of these are developed here. The authors also present in detail a number of important examples of Riemann surfaces of infinite genus (hyperelliptic surfaces of infinite genus, heat surfaces and Fermi surfaces). The book is suitable for graduate students and research mathematicians interested in analysis and integrable systems.
Download or read book Integrable Systems written by N.J. Hitchin and published by Oxford University Press, USA. This book was released on 2013-03-14 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.
Download or read book Probability Geometry and Integrable Systems written by Mark Pinsky and published by Cambridge University Press. This book was released on 2008-03-17 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflects the range of mathematical interests of Henry McKean, to whom it is dedicated.
Download or read book Integrable Systems written by Sergeĭ Petrovich Novikov and published by Cambridge University Press. This book was released on 1981-09-17 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers the theory of 'integrable' non-linear partial differential equations. The theory was developed at first by mathematical physicists but later mathematicians, particularly from the Soviet Union, were attracted to the field. In this volume are reprinted some fundamental contributions, originally published in Russian Mathematical Surveys, from some of the leading Soviet workers. Dr George Wilson has written an introduction intended to smooth the reader's path through some of the articles.
Download or read book Henry P McKean Jr Selecta written by F. Alberto Grünbaum and published by Birkhäuser. This book was released on 2015-12-31 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a selection of papers by Henry P. McKean, which illustrate the various areas in mathematics in which he has made seminal contributions. Topics covered include probability theory, integrable systems, geometry and financial mathematics. Each paper represents a contribution by Prof. McKean, either alone or together with other researchers, that has had a profound influence in the respective area.
Download or read book Combinatorial Theory of the Free Product with Amalgamation and Operator Valued Free Probability Theory written by Roland Speicher and published by American Mathematical Soc.. This book was released on 1998 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free probability theory, introduced by Voiculescu, has developed very actively in the last few years and has had an increasing impact on quite different fields in mathematics and physics. Whereas the subject arose out of the field of von Neumann algebras, presented here is a quite different view of Voiculescu's amalgamated free product. This combinatorial description not only allows re-proving of most of Voiculescu's results in a concise and elegant way, but also opens the way for many new results. Unlike other approaches, this book emphasizes the combinatorial structure of the concept of ``freeness''. This gives an elegant and easily accessible description of freeness and leads to new results in unexpected directions. Specifically, a mathematical framework for otherwise quite ad hoc approximations in physics emerges.
Download or read book Nonlinear Physics Theory And Experiment Nature Structure And Properties Of Nonlinear Phenomena Proceedings Of The First Conference written by Eleonora Alfinito and published by World Scientific. This book was released on 1996-06-20 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the Workshop 'Nonlinear Physics. Theory and Experiment' held in Gallipoli (Lecce, Italy) from June 29 to July 7, 1995.The purpose of the Workshop was to bring together scientists whose common interest is the nature, structure and properties of nonlinear phenomena in various areas of physics and applied mathematics.The purpose of the Workshop was to bring together scientists whose common interest is the nature, structure and properties of nonlinear phenomena in various areas of physics and applied mathematics.In fact, topics covered at the Workshop run from nonlinear optics to molecular dynamics, plasma waves, hydrodynamics, quantum electronics and solid state, and from inverse scattering transform methods to dynamical systems including integrability, hamiltonian structures, geometrical aspects, turbulence and chaos.
Download or read book Extended Affine Lie Algebras and Their Root Systems written by Bruce Normansell Allison and published by American Mathematical Soc.. This book was released on 1997 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is about extended affine Lie algebras (EALA's) and their root systems. EALA's were introduced by Høegh-Krohn and Torresani under the name irreducible quasi-simple Lie algebras. The major objective is to develop enough theory to provide a firm foundation for further study of EALA's. The first chapter of the paper is devoted to establishing some basic structure theory. It includes a proof of the fact that, as conjectured by Kac, the invariant symmetric bilinear form on an EALA can be scaled so that its restriction to the real span of the root system is positive semi-definite. The second chapter studies extended affine root systems (EARS) which are an axiomatized version of the root systems arising from EALA's. The concept of a semilattice is used to give a complete description of EARS. In the final chapter, a number of new examples of extended affine Lie algebras are given. The concluding appendix contains an axiomatic characterization of the nonisotropic roots in an EARS in a more general context than the one used in the rest of the paper.
Download or read book Moscow Seminar in Mathematical Physics written by A. Yu Morozov and published by American Mathematical Soc.. This book was released on 1999 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book The Integral Manifolds of the Three Body Problem written by Christopher Keil McCord and published by American Mathematical Soc.. This book was released on 1998 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The phase space of the spatial three-body problem is an open subset in R18. Holding the ten classical integrals of energu, center of mass, linear and angular momentum fixed defines an eight dimensional manifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the well-known bifurcations due to central configurations, and three are due to "critical points at infinity". This disproves Birkhoffs conjecture that the bifurcations occur only at central configurations.
Download or read book Differential and Integral Equations written by and published by . This book was released on 2001 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stratifying Endomorphism Algebras written by Edward Cline and published by American Mathematical Soc.. This book was released on 1996 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a systematic study of the relationships between the representation theories of [italic capital]R and [italic capital]A, especially those involving actual or potential quasi-hereditary structures on the latter algebra. Our original motivation comes from the theory of Schur algebras, work of Soergel on the Bernstein-Gelfand-Gelfand category [script capital]O, and resent results of Dlab-Heath-Marko realizing certain endomorphism algebras as quasi-hereditary algebras. We synthesize common features of all these examples, and go beyond them in a number of new directions.
Download or read book The Operator Hilbert Space OH Complex Interpolation and Tensor Norms written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1996 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recently developed duality theory of operator spaces, bounded operators are replaced by 'completely bounded' ones, isomorphism by 'complete isomorphisms' and Banach spaces by 'operator spaces'. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into [italic capital]B([italic capital]H) (with H being Hilbert). One of the main results is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (which we denote by [italic capitals]OH) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces.
Download or read book Crossed Products of von Neumann Algebras by Equivalence Relations and Their Subalgebras written by Igor Fulman and published by American Mathematical Soc.. This book was released on 1997 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author introduces and studies the construction of the crossed product of a von Neumann algebra. This construction is the generalization of the construction of the crossed product of an abelian von Neumann algebra by an equivalence relation introduced by J. Feldman and C. C. Moore. Many properties of this construction are proved in the general case. In addition, the generalizations of the Spectral Theorem on Bimodules and of the theorem on dilations are proved.
Download or read book Perturbation Theory in Periodic Problems for Two Dimensional Integrable Systems written by I. M. Krichever and published by CRC Press. This book was released on 1992 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
