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Author: Giovanni Gallavotti
Publisher: Springer Science & Business Media
ISBN: 3662058537
Category : Mathematics
Languages : en
Pages : 439
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Book Description
Intended for beginners in ergodic theory, this introductory textbook addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM Theroy. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Author: Giovanni Gallavotti
Publisher: Springer Science & Business Media
ISBN: 3662058537
Category : Mathematics
Languages : en
Pages : 439
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Book Description
Intended for beginners in ergodic theory, this introductory textbook addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM Theroy. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.
Author: Giuseppe Gaeta
Publisher: Springer Nature
ISBN: 1071626213
Category : Science
Languages : en
Pages : 601
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Book Description
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.
Author: Robert A. Meyers
Publisher: Springer Science & Business Media
ISBN: 1461418054
Category : Mathematics
Languages : en
Pages : 1885
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Book Description
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Author: Jialin Hong
Publisher: Springer Nature
ISBN: 9813290692
Category : Mathematics
Languages : en
Pages : 229
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Book Description
This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.
Author: Philippe Andre Martin
Publisher: Springer Science & Business Media
ISBN: 3662084902
Category : Science
Languages : en
Pages : 442
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Book Description
Emphasis is placed on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas within different domains of physics. Starting from a basic knowledge of quantum mechanics and classical electromagnetism, the exposition is self-contained and explicitly details all steps of the derivations. The new edition features a substantially new treatment of nucleon pairing.
Author: Errico Presutti
Publisher: Springer Science & Business Media
ISBN: 3540733051
Category : Mathematics
Languages : en
Pages : 478
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Book Description
Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.
Author: Martin Schlichenmaier
Publisher: Springer Science & Business Media
ISBN: 3540711759
Category : Science
Languages : en
Pages : 228
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Book Description
This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.
Author: Francisco J. Yndurain
Publisher: Springer Science & Business Media
ISBN: 3540332103
Category : Science
Languages : en
Pages : 484
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Book Description
First published in 1983, this book has become a classic among advanced textbooks. The new fourth edition maintains the high standard of its predecessors. The book offers basic knowledge of field theory and particle phenomenology. The author presents the basic facts of quark and gluon physics in pedagogical form. Explanations of theory are supported throughout with experimental findings. The text provides readers with sufficient understanding to follow modern research articles. This fourth edition presents a new section on heavy quark effective theories, more material on lattice QCD and on chiral perturbation theory.
Author: Jouni Suhonen
Publisher: Springer Science & Business Media
ISBN: 3540488618
Category : Science
Languages : en
Pages : 655
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Book Description
From Nucleons to Nucleus deals with single-particle and collective features of spherical nuclei. Each nuclear model is introduced and derived in detail. The formalism is then applied to light and medium-heavy nuclei in worked-out examples, and finally the acquired skills are strengthened by a wide selection of exercises, many relating the models to experimental data. Nuclear properties are discussed using particles, holes and quasi-particles. From Nucleons to Nucleus is based on lectures on nuclear physics given by the author, and serves well as a textbook for advanced students. Researchers too will appreciate it as a well-balanced reference to theoretical nuclear physics.
Author: Pierre Collet
Publisher: Springer Science & Business Media
ISBN: 3540347062
Category : Mathematics
Languages : en
Pages : 238
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Book Description
The study of dynamical systems is a well established field. This book provides a panorama of several aspects of interest to mathematicians and physicists. It collects the material of several courses at the graduate level given by the authors, avoiding detailed proofs in exchange for numerous illustrations and examples. Apart from common subjects in this field, a lot of attention is given to questions of physical measurement and stochastic properties of chaotic dynamical systems.
