Nonlinear Dynamical Systems Of Mathematical Physics Spectral And Symplectic Integrability Analysis
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Nonlinear Dynamical Systems Of Mathematical Physics
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Author : Denis L. Blackmore
language : en
Publisher: World Scientific
Release Date : 2011
Nonlinear Dynamical Systems Of Mathematical Physics written by Denis L. Blackmore and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville?Arnold and Mischenko?Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham?Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.
Symplectic Integration Of Stochastic Hamiltonian Systems
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Author : Jialin Hong
language : en
Publisher: Springer Nature
Release Date : 2023-02-21
Symplectic Integration Of Stochastic Hamiltonian Systems written by Jialin Hong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-21 with Mathematics categories.
This book provides an accessible overview concerning the stochastic numerical methods inheriting long-time dynamical behaviours of finite and infinite-dimensional stochastic Hamiltonian systems. The long-time dynamical behaviours under study involve symplectic structure, invariants, ergodicity and invariant measure. The emphasis is placed on the systematic construction and the probabilistic superiority of stochastic symplectic methods, which preserve the geometric structure of the stochastic flow of stochastic Hamiltonian systems. The problems considered in this book are related to several fascinating research hotspots: numerical analysis, stochastic analysis, ergodic theory, stochastic ordinary and partial differential equations, and rough path theory. This book will appeal to researchers who are interested in these topics.
Geometric Methods In Physics Xxxviii
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Author : Piotr Kielanowski
language : en
Publisher: Springer Nature
Release Date : 2020-10-27
Geometric Methods In Physics Xxxviii written by Piotr Kielanowski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-27 with Mathematics categories.
The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Geometric Methods In Physics Xl
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Author : Piotr Kielanowski
language : en
Publisher: Springer Nature
Release Date : 2024-08-27
Geometric Methods In Physics Xl written by Piotr Kielanowski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-27 with Science categories.
This volume collects papers based on lectures given at the XL Workshop on Geometric Methods in Physics, held in Białowieża, Poland in July 2023. These chapters provide readers an overview of cutting-edge research in infinite-dimensional groups, integrable systems, quantum groups, Lie algebras and their generalizations and a wide variety of other areas. Specific topics include: Yang-Baxter equation The restricted Siegel disc and restricted Grassmannian Geometric and deformation quantization Degenerate integrability Lie algebroids and groupoids Skew braces Geometric Methods in Physics XL will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.
Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds
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Author : A.K. Prykarpatsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Algebraic Integrability Of Nonlinear Dynamical Systems On Manifolds written by A.K. Prykarpatsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Science categories.
In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).
Global Analysis
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Author : M. Grmela
language : en
Publisher: Springer
Release Date : 2006-11-15
Global Analysis written by M. Grmela and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Lectures On Geometric Methods In Mathematical Physics
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Author : Jerrold E. Marsden
language : en
Publisher: SIAM
Release Date : 1981-01-01
Lectures On Geometric Methods In Mathematical Physics written by Jerrold E. Marsden and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Science categories.
A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.
Integrable Systems On Lie Algebras And Symmetric Spaces
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Author : A. T. Fomenko
language : en
Publisher: CRC Press
Release Date : 1988
Integrable Systems On Lie Algebras And Symmetric Spaces written by A. T. Fomenko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Second volume in the series, translated from the Russian, sets out new regular methods for realizing Hamilton's canonical equations in Lie algebras and symmetric spaces. Begins by constructing the algebraic embeddings in Lie algebras of Hamiltonian systems, going on to present effective methods for constructing complete sets of functions in involution on orbits of coadjoint representations of Lie groups. Ends with the proof of the full integrability of a wide range of many- parameter families of Hamiltonian systems that allow algebraicization. Annotation copyrighted by Book News, Inc., Portland, OR
Wolf Prize In Mathematics
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Author : Shiing-Shen Chern
language : en
Publisher: World Scientific
Release Date : 2000
Wolf Prize In Mathematics written by Shiing-Shen Chern and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Mathematics Of Complexity And Dynamical Systems
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05
Mathematics Of Complexity And Dynamical Systems written by Robert A. Meyers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-05 with Mathematics categories.
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.