Format: Hardback, 472 pages, height x width: 235x155 mm, 6 Illustrations, color;
2 Illustrations, black and white; X, 472 p. 8 illus., 6 illus. in color
Pub. Date: 25-May-2024
This is the sixth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where different types of mathematical problems converge, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects.
This Volume VI goes together with Volume V and focuses on singular holomorphic foliations, which is a multidisciplinary field and a whole area of mathematics in itself. Singular foliations arise, for instance, by considering:
The fibers of a smooth map between differentiable manifolds, with singularities at the critical points.
The integral lines of a vector field, or the action of a Lie group on a manifold. The singularities are the orbits with special isotropy.
The kernel of appropriate 1-forms. The singularities are the zeroes of the form.
Open books, which naturally appear in singularity theory, are foliations with singular set the binding.
These important examples highlight the deep connections between foliations and singularity theory. This volume consists of nine chapters, authored by world experts, which provide in-depth and reader-friendly introductions to some of the foundational aspects of the theory. These introductions also give insights into important lines of further research. Volume VI ends with an Epilogue by one of the current world leaders in the theory of complex foliations, with plenty of open questions and ideas for further research.
The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
1 Adolfo Guillot, On the singularities of complete holomorphic vector
fields in dimension two.- 2 Julio Rebelo and Helena Reis, Singularities of
holomorphic vector fields in dimensions 3: results and problems.- 3 Alcides
Lins Neto, Codimension one holomorphic Foliations.- 4 Maurcio Correa,
Analytic varieties invariant by holomorphic foliations and Pfaff systems.- 5
Felipe Cano and Beatriz Molina-Samper, Local Invariant Hypersurfaces for
Singular Foliations.- 6 Isao Nakai, From the perspective of nonsolvable
dynamics on (C, 0): Basics and Applications.- 7 Javier Ribon, Description of
the Zariski-closure of a group of formal diffeomorphisms.- 8 Frank Loray, The
Riemann-Hilbert correspondence for rank 2 meromorphic connections on curves.-
9 Emmanuel Paul, Jean-Pierre Ramis, Dynamics of the fifth Painleve
foliation.- 10 Jean-Pierre Ramis, Epilogue: Stokes phenomena. Dynamics,
Classification Problems and Avatars.
Format: Hardback, 309 pages, height x width: 235x155 mm, 5 Illustrations, color;
13 Illustrations, black and white; XVIII, 309 p. 18 illus., 5 illus. in color.
Series: CMS/CAIMS Books in Mathematics 10
Pub. Date: 24-Mar-2024
ISBN-13: 9783031530739
Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will be of interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.
Equations of Fluid dynamics and the shallow water
approximation.- Integrability and related analytical properties of nonlinear
PDE systems.- Analytical properties of some classical shallow-water
models.- Discussion.
Format: Hardback, 178 pages, height x width: 235x155 mm, 4 Illustrations, color;
52 Illustrations, black and white; X, 162 p. 56 illus., 4 illus. in color
Series: Latin American Mathematics Series
Pub. Date: 13-May-2024
ISBN-13: 9783031562242
This textbook offers a concise introduction to symplectic and contact geometry, with a focus on the relationships between these subjects and other topics such as Lie theory and classical mechanics.
Organized into four chapters, this work serves as a stepping stone for readers to delve into the subject, providing a succinct and motivating foundation. The content covers definitions, symplectic linear algebra, symplectic and contact manifolds, Hamiltonian systems, and more. Prerequisite knowledge includes differential geometry, manifolds, algebraic topology, de Rham cohomology, and the basics of Lie groups. Quick reviews are included where necessary, and examples and constructions are provided to foster understanding.
Ideal for advanced undergraduate students and graduate students, this volume can also serve as a valuable resource for independent researchers seeking a quick yet solid understanding of symplectic and contact geometry.
Preface.- Symplectic linear algebra.- Symplectic manifolds.- Hamiltonian
systems.- Contact manifolds.- References.- Index.
Format: Hardback, 140 pages, height x width: 235x155 mm, 2 Illustrations, color;
21 Illustrations, black and white; VIII, 204 p. 23 illus., 2 illus. in color.,
Pub. Date: 28-May-2024
ISBN-13: 9783031552014
This book serves as a textbook for an analytical mechanics course, a fundamental subject of physics, that pays special attention to important topics that are not discussed in most standard textbooks. Readers are provided with a clear understanding of topics that are usually inaccessible to the undergraduate level and that are critical to learning Lagrangian and Hamiltonian mechanics. Each chapter also includes worked problems and solutions, as well as additional exercises for readers to try.
This book begins with the fundamentals of analytical mechanics, concisely introducing readers to the calculus of variations, Hamiltons Principle, and Lagranges equations. While presenting readers with these core topics, the author uses an intuitive approach to delve into essential questions, such as where Galilean invariance lies in Lagrangian mechanics and how Hamiltons Principle of Least Action encompasses Newtons three laws, interesting conclusions that often go unnoticed. Infact, Hamiltons principle is taken throughout as the very origin of classical physical laws, and the choice of appropriate Lagrangians in each case as the real theoretical challenge, meaning that forms of Lagrangian which differ from the standard one are not mere curiosities but, instead, the general rule.
This book clarifies common misunderstandings that students face when learning the subject and formally rationalizes concepts that are often difficult to grasp. In addition, the final chapter provides an introduction to a Lagrangian field theory for those interested in learning more advanced topics. Ideal for upper undergraduate and graduate students, this book seeks to teach the intrinsic meaning of the principles and equations taught in an analytical mechanics course and convey their usefulness as powerful theoretical instruments of modern physics.
Chapter 1: Fundamentals.
Chapter 2: Lagrangian mechanics with L = T
V.
Chapter 3: Hamiltonian mechanics.
Chapter 4: Lagrangian and Hamiltonian
introduction of field theory.
Format: Paperback / softback, 235 pages, height x width: 235x155 mm, 3 Illustrations, color;
18 Illustrations, black and white; Approx. 235 p. 21 illus., 3 illus. in color.
Series: Universitext
Pub. Date: 09-Jun-2024
ISBN-13: 9789819720552
This book provides a new, comprehensive, and self-contained account of Oka theory as an introduction to function theory of several complex variables, mainly concerned with the Three Big Problems (Approximation, Cousin, Pseudoconvexity) that were solved by Kiyoshi Oka and form the basics of the theory. The purpose of the volume is to serve as a textbook in lecture courses right after complex function theory of one variable. The presentation aims to be readable and enjoyable both for those who are beginners in mathematics and for researchers interested in complex analysis in several variables and complex geometry.
The nature of the present book is evinced by its approach following Okas unpublished five papers of 1943 with his guiding methodological principle termed the Joku-Iko Principle, where historically the Pseudoconvexity Problem (Hartogs, Levi) was first solved in all dimensions, even for unramified Riemann domains as well.
The method that is used in the book is elementary and direct, not relying on the cohomology theory of sheaves nor on the L2--bar method, but yet reaches the core of the theory with the complete proofs.
Two proofs for Levis Problem are provided: One is Okas original with the Fredholm integral equation of the second kind combined with the Joku-Iko Principle, and the other is Grauerts by the well-known bumping-method with L. Schwartzs Fredholm theorem, of which a self-contained, rather simple and short proof is given. The comparison of them should be interesting even for specialists.
In addition to the Three Big Problems, other basic material is dealt with, such as Poincares non-biholomorphism between balls and polydisks, the CartanThullen theorem on holomorphic convexity, Hartogs separate analyticity, Bochners tube theorem, analytic interpolation, and others.
It is valuable for students and researchers alike to look into the original works of Kiyoshi Oka, which are not easy to find in books or monographs.
1 Holomorphic Functions.- 2 Coherent Sheaves and Okas Joku-Iko
Principle.- 3 Domains of Holomorphy.- 4 Pseudoconvex Domains I Problem and
Reduction.- 5 Pseudoconvex Domains II Solution.
Format: Hardback, 360 pages, height x width: 235x155 mm, 22 Illustrations, color;
10 Illustrations, black and white; XVI, 360 p. 32 illus., 22 illus. in color.
Series: SEMA SIMAI Springer Series 34
Pub. Date: 09-Jun-2024
ISBN-13: 9783031552595
The present volume contains a selection of papers from the XVIII International Conference on Hyperbolic Problems: Theory, Numerics, and Applications (HYP2022), which was held on June 20-24, 2022 in M?laga (Spain). The goal of this series of conferences is to bring together scientists with interests in the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models. The chapters in this volume correspond to some of the plenary lectures and to selected contributions related to theoretical aspects.
Format: Hardback, 436 pages, height x width: 235x155 mm, 122 Illustrations, color;
15 Illustrations, black and white; XVI, 436 p. 137 illus., 122 illus. in color.
Series: SEMA SIMAI Springer Series 35
Pub. Date: 09-Jun-2024
ISBN-13: 9783031552632
The present volume contains a selection of papers from the XVIII International Conference on Hyperbolic Problems: Theory, Numerics, and Applications (HYP2022), which was held on June 20-24, 2022 in M?laga (Spain). The goal of this series of conferences is to bring together scientists with interests in the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models. The chapters in this volume correspond to selected contributions related to numerical aspects and applications.