Download or read book Singularity Theory and Equivariant Symplectic Maps written by Thomas J. Bridges and published by Springer. This book was released on 2006-11-15 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate students in the areas of symplectic maps, Hamiltonian systems, singularity theory and equivariant bifurcation theory.

Download or read book Singularity Theory and Equivariant Symplectic Maps written by Thomas J. Bridges and published by . This book was released on 2014-01-15 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Singularities Bifurcations and Catastrophes written by James Montaldi and published by Cambridge University Press. This book was released on 2021-06-24 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, existence and uniqueness theorems for ODEs, and some basic material on rings and modules. Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided.

Download or read book Real and Complex Singularities written by James William Bruce and published by CRC Press. This book was released on 1999-08-26 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundaries of singularity theory are broad and vague, connecting the most important applications of mathematics and science with more abstract areas. Optics, robotics, computer vision, Hamiltonian mechanics, bifurcation theory and differential equations are among the variety of topics that benefit from developments in the theory. With singularity theory encompassing more and more applications, Real and Complex Singularities provides insight into the future of this expanding field. Comprising refereed contributions to the Fifth Workshop on Real and Complex Singularities, this volume addresses three important areas related to the broad subject of singularities. The first section deals with questions within singularity theory itself, representing the topics currently being investigated. The second explores applications of singularity theory to differential geometry, robotics, and computer vision. The final section consists of applications to bifurcation theory and dynamical systems. With over two-hundred tables that provide quick access to data, this volume is a complete overview of the most current topics and applications of singularity theory. Real and Complex Singularities creates the opportunity for you to stay up-to-date with recent advances and discover promising directions for future research in the field.

Download or read book Real and Complex Singularities written by Jean-Paul Brasselet and published by Springer Science & Business Media. This book was released on 2007-01-05 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers presented at the eighth São Carlos Workshop on Real and Complex Singularities, held at the IML, Marseille, July 2004. Like the workshop, this collection establishes the state of the art and presents new trends, new ideas and new results in all of the branches of singularities. Real and Complex Singularities offers a useful summary of leading ideas in singularity theory, and inspiration for future research.

Download or read book Kodaira Spencer Maps in Local Algebra written by Bernd Herzog and published by Springer. This book was released on 2006-11-14 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph contributes to Lech's inequality - a 30-year-old problem of commutative algebra, originating in the work of Serre and Nagata, that relates the Hilbert function of the total space of an algebraic or analytic deformation germ to the Hilbert function of the parameter space. A weakened version of Lech's inequality is proved using a construction that can be considered as a local analog of the Kodaira-Spencer map known from the deformation theory of compact complex manifolds. The methods are quite elementary, and will be of interest for researchers in deformation theory, local singularities and Hilbert functions.

Download or read book Equivariant Sheaves and Functors written by Joseph Bernstein and published by Springer. This book was released on 2006-11-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equivariant derived category of sheaves is introduced. All usual functors on sheaves are extended to the equivariant situation. Some applications to the equivariant intersection cohomology are given. The theory may be useful to specialists in representation theory, algebraic geometry or topology.

Download or read book New Trends For Hamiltonian Systems And Celestial Mechanics written by Lacomba Ernesto A and published by #N/A. This book was released on 1996-07-03 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume puts together several important lectures on the Hamiltonian Systems and Celestial Mechanics to form a comprehensive and authoritative collection of works on the subject. Their relationship to several aspects of topology, mechanics and dynamical systems in general are also emphasized. The papers presented are an outgrowth of the lectures that took place during the “International Symposium on Hamiltonian Systems and Celestial Mechanics ”, which was held at Cocoyoc (Morelos, México) from September 13 to 17, 1994.

Download or read book Extended Abstracts Spring 2014 written by Montserrat Corbera and published by Birkhäuser. This book was released on 2015-10-20 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two parts of the present volume contain extended conference abstracts corresponding to selected talks given by participants at the "Conference on Hamiltonian Systems and Celestial Mechanics 2014" (HAMSYS2014) (15 abstracts) and at the "Workshop on Virus Dynamics and Evolution" (12 abstracts), both held at the Centre de Recerca Matemàtica (CRM) in Barcelona from June 2nd to 6th, 2014, and from June 23th to 27th, 2014, respectively. Most of them are brief articles, containing preliminary presentations of new results not yet published in regular research journals. The articles are the result of a direct collaboration between active researchers in the area after working in a dynamic and productive atmosphere. The first part is about Central Configurations, Periodic Orbits and Hamiltonian Systems with applications to Celestial Mechanics – a very modern and active field of research. The second part is dedicated to mathematical methods applied to viral dynamics and evolution. Mathematical modelling of biological evolution currently attracts the interest of both mathematicians and biologists. This material offers a variety of new exciting problems to mathematicians and reasonably inexpensive mathematical methods to evolutionary biologists. It will be of scientific interest to both communities. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

Download or read book Potential Theory on Infinite Networks written by Paolo M. Soardi and published by Springer. This book was released on 2006-11-15 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds. The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.

Download or read book Lectures on Probability Theory written by Dominique Bakry and published by Springer. This book was released on 2006-11-15 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains work-outs of the notes of three 15-hour courses of lectures which constitute surveys on the concerned topics given at the St. Flour Probability Summer School in July 1992. The first course, by D. Bakry, is concerned with hypercontractivity properties and their use in semi-group theory, namely Sobolev and Log Sobolev inequa- lities, with estimations on the density of the semi-groups. The second one, by R.D. Gill, is about statistics on survi- val analysis; it includes product-integral theory, Kaplan- Meier estimators, and a look at cryptography and generation of randomness. The third one, by S.A. Molchanov, covers three aspects of random media: homogenization theory, loca- lization properties and intermittency. Each of these chap- ters provides an introduction to and survey of its subject.

Download or read book Nonlinear Potential Theory and Weighted Sobolev Spaces written by Bengt O. Turesson and published by Springer Science & Business Media. This book was released on 2000-06-21 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.

Download or read book Potential Theory Selected Topics written by Hiroaki Aikawa and published by Springer. This book was released on 2006-11-14 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of these lecture notes is an introduction to potential theory to prepare the reader for later parts, which can be used as the basis for a series of advanced lectures/seminars on potential theory/harmonic analysis. Topics covered in the book include minimal thinness, quasiadditivity of capacity, applications of singular integrals to potential theory, L(p)-capacity theory, fine limits of the Nagel-Stein boundary limit theorem and integrability of superharmonic functions. The notes are written for an audience familiar with the theory of integration, distributions and basic functional analysis.

Download or read book Bifurcations in Hamiltonian Systems written by Henk Broer and published by Springer. This book was released on 2003-01-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.

Download or read book Topics in the Theory of Riemann Surfaces written by Robert D.M. Accola and published by Springer. This book was released on 2006-11-14 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.

Download or read book Algebraic Cycles and Hodge Theory written by Mark L. Green and published by Springer Science & Business Media. This book was released on 1994-12-16 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.

Download or read book Finsler Metrics A Global Approach written by Marco Abate and published by Springer. This book was released on 2006-11-15 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. After reviewing real Finsler geometry stressing global results, complex Finsler geometry is presented introducing connections, Kählerianity, geodesics, curvature. Finally global geometry and complex Monge-Ampère equations are discussed for Finsler manifolds with constant holomorphic curvature, which are important in geometric function theory. Following E. Cartan, S.S. Chern and S. Kobayashi, the global approach carries the full strength of hermitian geometry of vector bundles avoiding cumbersome computations, and thus fosters applications in other fields.