Singularities & Dynamical Systems PDF Download

Author: S.N. Pnevmatikos
Publisher: Elsevier
ISBN: 008087214X
Category : Mathematics
Languages : en
Pages : 467

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Book Description
This volume is an account of the lectures delivered at the international Conference ``Singularities and Dynamical Systems-83''. The main purpose of the Conference was to create conditions of scientific contact between mathematicians and physicists who have singularities and dynamical systems as common interests.

Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 3662067986
Category : Mathematics
Languages : en
Pages : 241

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Book Description
This book is devoted to applications of singularity theory in mathematics and physics, covering a broad spectrum of topics and problems. "The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures." --ZENTRALBLATT MATH

Author: Gert-Martin Greuel
Publisher: Springer Science & Business Media
ISBN: 3540284192
Category : Mathematics
Languages : en
Pages : 482

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Book Description
Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.

Author: Vladimir Igorevich Arnolʹd
Publisher: Cambridge University Press
ISBN: 9780521422802
Category : Mathematics
Languages : en
Pages : 88

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Book Description
In this book, which is based on lectures given in Pisa under the auspices of the Accademia Nazionale dei Lincei, the distinguished mathematician Vladimir Arnold describes those singularities encountered in different branches of mathematics. He avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear, such as geometry and optics; optimal control theory and algebraic geometry; reflection groups and dynamical systems and many more. This will be an excellent companion for final year undergraduates and graduates whose area of study brings them into contact with singularities.

Author: V.I. Arnold
Publisher: Springer Science & Business Media
ISBN: 1461251540
Category : Mathematics
Languages : en
Pages : 390

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Book Description
... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).

Author: Yangsheng Xu
Publisher: Springer Science & Business Media
ISBN: 1461535883
Category : Technology & Engineering
Languages : en
Pages : 291

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Book Description
Robotic technology offers two potential benefits for future space exploration. One benefit is minimizing the risk that astronauts face. The other benefit is increasing their productivity. Realizing the benefits of robotic technology in space will require solving several problems which are unique and now becoming active research topics. One of the most important research areas is dynamics, control, motion and planning for space robots by considering the dynamic interaction between the robot and the base (space station, space shuttle, or satellite). Any inefficiency in the planning and control can considerably risk by success of the space mission. Space Robotics: Dynamics and Control presents a collection of papers concerning fundamental problems in dynamics and control of space robots, focussing on issues relevant to dynamic base/robot interaction. The authors are all pioneers in theoretical analysis and experimental systems development of space robot technology. The chapters are organized within three problem areas: dynamics problems, nonholonomic nature problems, and control problems. This collection provides a solid reference for researchers in robotics, mechanics, control, and astronautical science.

Author: Vladimir Igorevich Arnolʹd
Publisher:
ISBN: 9781470445485
Category : Singularities (Mathematics)
Languages : en
Pages : 346

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Book Description
The theory of singularities lies at the crossroads between those branches of mathematics which are the most abstract and those which are the most applied. Algebraic and differential geometry and topology, commutative algebra and group theory are as intimately connected to singularity theory as are dynamical systems theory, control theory, differential equations, quantum mechanical and quasi-classical asymptotics, optics, and functional analysis. This collection of papers incorporates recent results of participants in the editor's ongoing seminar in singularity theory, held in the Mechanics and.

Author: James William Bruce
Publisher: CRC Press
ISBN: 9781584881421
Category : Mathematics
Languages : en
Pages : 292

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Book Description
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.

Author: Steven Dale Cutkosky
Publisher: American Mathematical Soc.
ISBN: 0821835556
Category : Mathematics
Languages : en
Pages : 198

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Book Description
The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is truly a fundamental problem. It has a complete solution in characteristic zero and partial solutions in arbitrary characteristic. The resolution of singularities in characteristic zero is a key result used in many subjects besides algebraic geometry, such as differential equations, dynamical systems, number theory, the theory of $\mathcal{D}$-modules, topology, and mathematical physics. This book is a rigorous, but instructional, look at resolutions. A simplified proof, based on canonical resolutions, is given for characteristic zero. There are several proofs given for resolution of curves and surfaces in characteristic zero and arbitrary characteristic. Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing valuable insight and intuition for the novice (or expert). There are many examples and exercises throughout the text. The book is suitable for a second course on an exciting topic in algebraic geometry. A core course on resolutions is contained in Chapters 2 through 6. Additional topics are covered in the final chapters. The prerequisite is a course covering the basic notions of schemes and sheaves.

Author: Alexander N. Gorban
Publisher:
ISBN:
Category :
Languages : en
Pages : 52

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Book Description
The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters of the system and accuracy of relaxation. This system of times contains: the time before the first entering of the motion into -neighbourhood of the limit set, the time of final entering in this neighbourhood and the time of stay of the motion outside the -neighbourhood of the limit set. The singularities of relaxation times as functions of (, ) under fixed are studied. A classification of different bifurcations (explosions) of limit sets is performed. The bifurcations fall into those with appearance of new limit points and bifurcations with appearance of new limit sets at finite distance from the existing ones. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The peculiarities of transition processes under perturbations are studied. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for smooth two-dimensional structural stable systems.