Twist Mappings And Their Applications
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Twist Mappings And Their Applications
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Author : Richard McGehee
language : en
Publisher: Springer
Release Date : 1992-06-24
Twist Mappings And Their Applications written by Richard McGehee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-06-24 with Mathematics categories.
In his 1890 analysis of the stability of orbits in the classical three body problem, PoincarA(c) introduced basic ideas about twist maps of the annulus. One hundred years later, the study of twist maps is an important area of dynamical systems theory. Based on a recent IMA workshop, Twist Mappings and Their Applications presents some of the most up-to-date developments in this area by leading figures in the field. The topics in this volume range from the exposition of new tools used to study the area-preserving map of the two-dimensional annulus to analogues of twist maps for higher dimensional annuli and their applications to dynamical systems. In addition, the text incorporates articles which use such innovations to shed light on the original questions of stability in mechanical systems. This book will be of interest to mathematicians, physicists and engineers wishing to keep abreast of this fundamental and evolving area of classical mechanics. It could also be useful to students, scientists and scholars interested in studying the practice of manifold analysis.
Twist Mappings And Their Applications
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FREE 30 Days
Author : Richard McGehee
language : en
Publisher: Springer
Release Date : 1992
Twist Mappings And Their Applications written by Richard McGehee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Symplectic Twist Maps
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Author : Christophe Gol
language : en
Publisher: World Scientific
Release Date : 2001
Symplectic Twist Maps written by Christophe Gol and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This book concentrates mainly on the theorem of existence of periodic orbits for higher dimensional analogs of Twist maps. The setting is that of a discrete variational calculus and the techniques involve Conley-Zehnder-Morse Theory. They give rise to the concept of ghost tori which are of interest in the dimension 2 case (ghost circles). The debate is oriented somewhat toward the open problem of finding orbits of all (in particular, irrational) rotation vectors.
Construction Of Mappings For Hamiltonian Systems And Their Applications
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Author : Sadrilla S. Abdullaev
language : en
Publisher: Springer
Release Date : 2006-08-02
Construction Of Mappings For Hamiltonian Systems And Their Applications written by Sadrilla S. Abdullaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-02 with Science categories.
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.
Nonlinear Analysis And Its Applications To Differential Equations
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Author : M.R. Grossinho
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Analysis And Its Applications To Differential Equations written by M.R. Grossinho 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 2012-12-06 with Mathematics categories.
This work, consisting of expository articles as well as research papers, highlights recent developments in nonlinear analysis and differential equations. The material is largely an outgrowth of autumn school courses and seminars held at the University of Lisbon and has been thoroughly refereed. Several topics in ordinary differential equations and partial differential equations are the focus of key articles, including: * periodic solutions of systems with p-Laplacian type operators (J. Mawhin) * bifurcation in variational inequalities (K. Schmitt) * a geometric approach to dynamical systems in the plane via twist theorems (R. Ortega) * asymptotic behavior and periodic solutions for Navier--Stokes equations (E. Feireisl) * mechanics on Riemannian manifolds (W. Oliva) * techniques of lower and upper solutions for ODEs (C. De Coster and P. Habets) A number of related subjects dealing with properties of solutions, e.g., bifurcations, symmetries, nonlinear oscillations, are treated in other articles. This volume reflects rich and varied fields of research and will be a useful resource for mathematicians and graduate students in the ODE and PDE community.
Stability And Bifurcation Theory For Non Autonomous Differential Equations
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Author : Anna Capietto
language : en
Publisher: Springer
Release Date : 2012-12-14
Stability And Bifurcation Theory For Non Autonomous Differential Equations written by Anna Capietto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Mathematics categories.
This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.
Selected Chapters In The Calculus Of Variations
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Author : Jürgen Moser
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Selected Chapters In The Calculus Of Variations written by Jürgen Moser and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
0.1 Introduction These lecture notes describe a new development in the calculus of variations which is called Aubry-Mather-Theory. The starting point for the theoretical physicist Aubry was a model for the descrip tion of the motion of electrons in a two-dimensional crystal. Aubry investigated a related discrete variational problem and the corresponding minimal solutions. On the other hand, Mather started with a specific class of area-preserving annulus mappings, the so-called monotone twist maps. These maps appear in mechanics as Poincare maps. Such maps were studied by Birkhoff during the 1920s in several papers. In 1982, Mather succeeded to make essential progress in this field and to prove the existence of a class of closed invariant subsets which are now called Mather sets. His existence theorem is based again on a variational principle. Although these two investigations have different motivations, they are closely re lated and have the same mathematical foundation. We will not follow those ap proaches but will make a connection to classical results of Jacobi, Legendre, Weier strass and others from the 19th century. Therefore in Chapter I, we will put together the results of the classical theory which are the most important for us. The notion of extremal fields will be most relevant. In Chapter II we will investigate variational problems on the 2-dimensional torus. We will look at the corresponding global minimals as well as at the relation be tween minimals and extremal fields. In this way, we will be led to Mather sets.
Ergodic Theory
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Author : Idris Assani
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-06-20
Ergodic Theory written by Idris Assani and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.
This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Contents: Duality of the almost periodic and proximal relations Limit directions of a vector cocycle, remarks and examples Optimal norm approximation in ergodic theory The iterated Prisoner’s Dilemma: good strategies and their dynamics Lyapunov exponents for conservative twisting dynamics: a survey Takens’ embedding theorem with a continuous observable
Genetic Mapping And Dna Sequencing
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Author : Terry Speed
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Genetic Mapping And Dna Sequencing written by Terry Speed 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 2012-12-06 with Mathematics categories.
Genetics mapping, physical mapping and DNA sequencing are the three key components of the human and other genome projects. Statistics, mathematics and computing play important roles in all three, as well as in the uses to which the mapping and sequencing data are put. This volume edited by key researchers Mike Waterman and Terry Speed reviews recent progress in the area, with an emphasis on the theory and application of genetic mapping.
The Principle Of Least Action In Geometry And Dynamics
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Author : Karl Friedrich Siburg
language : en
Publisher: Springer
Release Date : 2004-04-30
The Principle Of Least Action In Geometry And Dynamics written by Karl Friedrich Siburg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-30 with Mathematics categories.
New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.