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Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics, Pettini Marco



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Автор: Pettini Marco
Название:  Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
ISBN: 9780387308920
Издательство: Springer
Классификация:
ISBN-10: 038730892X
Обложка/Формат: Hardback
Страницы: 472
Вес: 0.762 кг.
Дата издания: 28.08.2007
Серия: Interdisciplinary Applied Mathematics
Язык: English
Издание: 2007 ed.
Иллюстрации: 91 illustrations, black and white; xvi, 456 p. 91 illus.
Размер: 164 x 240 x 32
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
Рейтинг:
Поставляется из: Германии
Дополнительное описание: Формат: 235x155
Илюстрации: 91
Круг читателей: Researchers, graduate students
Ключевые слова:
Язык: eng
Оглавление: Foreword.- Preface.- Introduction.- Background in Physics.- Geometrization of Hamiltonian Dynamics.- Integrability.- Geometry and chaos.- Geometry of chaos and phase transitions.- Topological Hypothesis on the origin of phase transitions.- Geometry, topology and thermodynamics.- Phase transitions and topology: necessity theorems.- Phase transitions and topology: exact results.- Future developments.- Appendix 1: Elements of geometry and topology of differentiable manifolds.- Appendix 2: Elements of Riemannian geometry.- Appendix 3: Summary of elementary Morse theory.- References.





Calculus of Variations II / The Hamiltonian Formalism

Автор: Giaquinta Mariano, Hildebrandt Stefan
Название: Calculus of Variations II / The Hamiltonian Formalism
ISBN: 3540579613 ISBN-13(EAN): 9783540579618
Издательство: Springer
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Цена: 15009 р.
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Описание: This long-awaited book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e.g. from geometrical optics, of parts of the theory. A variety of aids to the reader is provided: besides the very detailed table of contents, an introduction to each chapter, section and subsection, an overview of the relevant literature (in Vol. 2) plus the references in the Scholia to each chapter, in the (historical) footnotes, and in the bibliography, and finally an index of the examples used throughout the book. Both individually and collectively these volumes have already become standard references.

Lagrangian and Hamiltonian Methods For Nonlinear Control / Proceedings from the 3rd IFAC Workshop, Nagoya, Japan, July 2006

Автор: Bullo Francesco, Fujimoto Kenji
Название: Lagrangian and Hamiltonian Methods For Nonlinear Control / Proceedings from the 3rd IFAC Workshop, Nagoya, Japan, July 2006
ISBN: 3540738894 ISBN-13(EAN): 9783540738893
Издательство: Springer
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Цена: 19056 р.
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Описание: From the contents: A Differential-Geometric Approach for Bernstein’s Degrees-of-Freedom Problem.- Nonsmooth Riemannian Optimization with Applications to Sphere Packing and Grasping.- Synchronization of Networked Lagrangian Systems.- An Algorithm to Discretize One-Dimensional Distributed Port Hamiltonian Systems.- Virtual Lagrangian Construction Method for Infinitedimensional Systems with Homotopy Operators.- Direct Discrete-Time Design for Sampled-Data Hamiltonian Control Systems.- Kinematic Compensation in Port-Hamiltonian Telemanipulation.- Interconnection and Damping Assignment Passivity-Based Control of a Four-Tank System.- Towards Power-based Control Strategies for a Class of Nonlinear Mechanical Systems.- Power Shaping Control of Nonlinear Systems: A Benchmark Example.- Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations via Coordinate Changes.- Simultaneous Interconnection and Damping Assignment Passivity–Based Control: Two Practical Examples.

Bifurcations in Hamiltonian Systems

Автор: Broer
Название: Bifurcations in Hamiltonian Systems
ISBN: 3540004033 ISBN-13(EAN): 9783540004035
Издательство: Springer
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Цена: 4037 р.
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Описание: 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, Grobner basis techniques, are applied.

The readership addressed consists of advanced graduate students and researchers in dynamical systems.

Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

Автор: Marco Pettini
Название: Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
ISBN: 1441921648 ISBN-13(EAN): 9781441921642
Издательство: Springer
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Цена: 12704 р.
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Описание: This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The subject of the book, which contains numerous illustrations throughout, is very original and nothing similar has been written hitherto.

The Geometry of Higher-Order Hamilton Spaces / Applications to Hamiltonian Mechanics

Автор: Miron R.
Название: The Geometry of Higher-Order Hamilton Spaces / Applications to Hamiltonian Mechanics
ISBN: 1402015747 ISBN-13(EAN): 9781402015748
Издательство: Springer
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Цена: 13859 р.
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Описание: This book is the first to present an overview of higher-order Hamilton geometry with applications to higher-order Hamiltonian mechanics. It is a direct continuation of the book The Geometry of Hamilton and Lagrange Spaces, (Kluwer Academic Publishers, 2001). It contains the general theory of higher order Hamilton spaces H(k)n, k>=1, semisprays, the canonical nonlinear connection, the N-linear metrical connection and their structure equations, and the Riemannian almost contact metrical model of these spaces. In addition, the volume also describes new developments such as variational principles for higher order Hamiltonians; Hamilton-Jacobi equations; higher order energies and law of conservation; Noether symmetries; Hamilton subspaces of order k and their fundamental equations. The duality, via Legendre transformation, between Hamilton spaces of order k and Lagrange spaces of the same order is pointed out. Also, the geometry of Cartan spaces of order k =1 is investigated in detail. This theory is useful in the construction of geometrical models in theoretical physics, mechanics, dynamical systems, optimal control, biology, economy etc.

Quantum Mechanics of Non-Hamiltonian and Dissipative Systems,7

Автор: Vasily Tarasov
Название: Quantum Mechanics of Non-Hamiltonian and Dissipative Systems,7
ISBN: 0444530916 ISBN-13(EAN): 9780444530912
Издательство: Elsevier Science
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Цена: 20213 р.
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Описание: Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006.

Solved Problems in Lagrangian and Hamiltonian Mechanics

Автор: Gignoux
Название: Solved Problems in Lagrangian and Hamiltonian Mechanics
ISBN: 9048123925 ISBN-13(EAN): 9789048123926
Издательство: Springer
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Цена: 9816 р.
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Описание: Intends to bridge the gap between the Newtonian mechanics and the studies on chaos. This title covers such topics as: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. It is suitable for undergraduate students as well as others whose work involves mechanics, physics and engineering in general.

Hamiltonian Mechanics of Gauge Systems

Автор: Prokhorov
Название: Hamiltonian Mechanics of Gauge Systems
ISBN: 052189512X ISBN-13(EAN): 9780521895125
Издательство: Cambridge Academ
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Цена: 14928 р.
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Описание: An introduction to Hamiltonian mechanics of systems with gauge symmetry for graduate students and researchers in theoretical and mathematical physics.

Open Quantum Systems I / The Hamiltonian Approach

Автор: Attal StГ©phane, Joye Alain, Pillet Claude-Alain
Название: Open Quantum Systems I / The Hamiltonian Approach
ISBN: 3540309918 ISBN-13(EAN): 9783540309918
Издательство: Springer
Цена: 6578 р.
Наличие на складе: Поставка под заказ.

Описание: Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. From a mathematical point of view, it involves a large body of knowledge. Significant progress in the understanding of such systems has been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. In Volume I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems.Volume II is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential equations, both in the classical and the quantum context, is provided. These mathematical tools are put into perspective with physical motivations and applications.Volume III is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.

Construction of Mappings for Hamiltonian Systems and Their Applications

Автор: Abdullaev Sadrilla S.
Название: Construction of Mappings for Hamiltonian Systems and Their Applications
ISBN: 3540309152 ISBN-13(EAN): 9783540309154
Издательство: Springer
Цена: 9239 р.
Наличие на складе: Поставка под заказ.

Описание: Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical problems described by Hamiltonian systems. It develops a new, mathematically-rigorous method to construct symplectic mappings which replaces the dynamics of continuous Hamiltonian systems by the discrete ones. Applications of the mapping methods encompass the chaos theory in non-twist and non-smooth dynamical systems, the structure and chaotic transport in the stochastic layer, the magnetic field lines in magnetically confinement devices of plasmas, ray dynamics in waveguides, etc. The book is intended for postgraduate students and researches, physicists and astronomers working in the areas of plasma physics, hydrodynamics, celestial mechanics, dynamical astronomy, and accelerator physics. It should also be useful for applied mathematicians involved in analytical and numerical studies of dynamical systems.

Metamorphoses of Hamiltonian Systems with Symmetries

Автор: Efstathiou Konstantinos
Название: Metamorphoses of Hamiltonian Systems with Symmetries
ISBN: 354024316X ISBN-13(EAN): 9783540243168
Издательство: Springer
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Цена: 4037 р.
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Описание: Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.

Nonlinear Oscillations of Hamiltonian PDEs

Автор: Berti Massimiliano
Название: Nonlinear Oscillations of Hamiltonian PDEs
ISBN: 0817646809 ISBN-13(EAN): 9780817646806
Издательство: Springer
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Цена: 12126 р.
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Описание: Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations.After introducing the reader to classical finite-dimensional dynamical system theory, including the Weinstein—Moser and Fadell—Rabinowitz bifurcation results, the analogous theory for nonlinear wave equations is developed. The theory and applications of the Nash—Moser theorem to a class of nonlinear wave equations is also discussed together with other basic notions of Hamiltonian PDEs and number theory. The main examples of Hamiltonian PDEs presented include: the nonlinear wave equation, the nonlinear SchrГ¶dinger equation, beam equations, and the Euler equations of hydrodynamics.This text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.


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