Loop Groups Discrete Versions Of Some Classical Integrable Systems And Rank 2 Extensions
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Loop Groups Discrete Versions Of Some Classical Integrable Systems And Rank 2 Extensions
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Author : Percy Deift
language : en
Publisher:
Release Date : 1992
Loop Groups Discrete Versions Of Some Classical Integrable Systems And Rank 2 Extensions written by Percy Deift and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Hamiltonian systems categories.
Loop Groups Discrete Versions Of Some Classical Integrable Systems And Rank 2 Extensions
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Author : Percy Deift
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Loop Groups Discrete Versions Of Some Classical Integrable Systems And Rank 2 Extensions written by Percy Deift and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
The theory of classical $R$-matrices provides a unified approach to the understanding of most, if not all, known integrable systems. This work, which is suitable as a graduate textbook in the modern theory of integrable systems, presents an exposition of $R$-matrix theory by means of examples, some old, some new. In particular, the authors construct continuous versions of a variety of discrete systems of the type introduced recently by Moser and Vesclov. In the framework the authors establish, these discrete systems appear as time-one maps of integrable Hamiltonian flows on co-adjoint orbits of appropriate loop groups, which are in turn constructed from more primitive loop groups by means of classical $R$-matrix theory. Examples include the discrete Euler-Arnold top and the billiard ball problem in an elliptical region in $n$ dimensions. Earlier results of Moser on rank 2 extensions of a fixed matrix can be incorporated into this framework, which implies in particular that many well-known integrable systems--such as the Neumann system, periodic Toda, geodesic flow on an ellipsoid, etc.--can also be analyzed by this method.
Separatrix Surfaces And Invariant Manifolds Of A Class Of Integrable Hamiltonian Systems And Their Perturbations
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Author : Jaume Llibre
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Separatrix Surfaces And Invariant Manifolds Of A Class Of Integrable Hamiltonian Systems And Their Perturbations written by Jaume Llibre and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the critical leaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonian perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of 'almost all' the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.
Extension Of Positive Definite Distributions And Maximum Entropy
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Author : Jean-Pierre Gabardo
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Extension Of Positive Definite Distributions And Maximum Entropy written by Jean-Pierre Gabardo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.
An Extension Of The Galois Theory Of Grothendieck
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Author : André Joyal
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
An Extension Of The Galois Theory Of Grothendieck written by André Joyal and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Computation And Combinatorics In Dynamics Stochastics And Control
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Author : Elena Celledoni
language : en
Publisher: Springer
Release Date : 2019-01-13
Computation And Combinatorics In Dynamics Stochastics And Control written by Elena Celledoni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-13 with Mathematics categories.
The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.
Littlewood Paley Theory On Spaces Of Homogeneous Type And The Classical Function Spaces
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Author : Yongsheng Han
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Littlewood Paley Theory On Spaces Of Homogeneous Type And The Classical Function Spaces written by Yongsheng Han and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calder 'on reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.
Random Perturbations Of Hamiltonian Systems
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Author : Mark Iosifovich Freĭdlin
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Random Perturbations Of Hamiltonian Systems written by Mark Iosifovich Freĭdlin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.
Degenerate Principal Series For Symplectic Groups
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Author : Chris Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Degenerate Principal Series For Symplectic Groups written by Chris Jantzen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This paper is concerned with induced representations for $p$-adic groups. In particular, Jantzen examines the question of reducibility in the case where the inducing subgroup is a maximal parabolic subgroup of $Sp_{2n (F)$ and the inducing representation is one-dimensional. Two different approaches to this problem are used. The first, based on the work of Casselman and of Gustafson, reduces the problem to the corresponding question about an associated finite-dimensional representation of a certain Hecke algebra. The second approach is based on a technique of Tadi\'c and involves an analysis of Jacquet modules. This is used to obtain a more general result on induced representations, which may be used to deal with the problem when the inducing representation satisfies a regularity condition. The same basic argument is also applied in a case-by-case fashion to nonregular cases.
Nonlinear Evolution Equations And Dynamical Systems Needs 94
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Author : Vladimir G Makhankov
language : en
Publisher: World Scientific
Release Date : 1995-04-26
Nonlinear Evolution Equations And Dynamical Systems Needs 94 written by Vladimir G Makhankov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-26 with categories.