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 Free Download Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935-2008) by Albert C. J. Luo, Valentin Afraimovich English | PDF | 2010 | 312 Pages | ISBN : 3642127177 | 33.8 MB "Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935-2008)" covers the recent developments and advances in the theory and application of Hamiltonian chaos in nonlinear Hamiltonian systems. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. Each chapter in this book was written by well-established scientists in the field of nonlinear Hamiltonian systems. The development presented in this book goes beyond the KAM theory, and the onset and disappearance of chaos in the stochastic and resonant layers of nonlinear Hamiltonian systems are predicted analytically, instead of qualitatively. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.  Free Download Metamorphoses of Hamiltonian Systems with Symmetries by Konstantinos Efstathiou English | PDF | 2005 | 155 Pages | ISBN : 354024316X | 3.5 MB 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.  Free Download Classical Mechanics: Systems of Particles and Hamiltonian Dynamics by Walter Greiner English | PDF (True) | 2010 | 574 Pages | ISBN : 3642034330 | 7.5 MB This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles to realistic problems.  Free Download The Sequential Quadratic Hamiltonian Method: Solving Optimal Control Problems English | 2023 | ISBN: 036771552X | 267 Pages | PDF (True) | 7.2 MB The sequential quadratic hamiltonian (SQH) method is a novel numerical optimization procedure for solving optimal control problems governed by differential models. It is based on the characterisation of optimal controls in the framework of the Pontryagin maximum principle (PMP).  Symplectic Integration of Stochastic Hamiltonian Systems English | 2023 | ISBN: 9811976694 | 312 Pages | EPUB (True)/PDF | 28 MB 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.  Sergei B. Kuksin, "Analysis of Hamiltonian PDEs" English | 2000 | pages: 224 | ISBN: 0198503954 | DJVU | 1,7 mb For the last 20-30 years, interest among mathematicians and physicists in infinite-dimensional Hamiltonian systems and Hamiltonian partial differential equations has been growing strongly, and many papers and a number of books have been written on integrable Hamiltonian PDEs. During the last  Bifurcations in Hamiltonian Systems: Computing Singularities by Gröbner Bases by Henk Broer English | PDF | 2003 | 178 Pages | ISBN : 3540004033 | 3.5 MB 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.
 English | 2021 | ISBN: 978-3110667226 | 394 pages | pdf, epub | 59.5 MB The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.  Hamiltonian Dynamical Systems by R.S MacKay, J.D Meiss English | 1987 | ISBN: 0852742053 | 784 pages | DJVU | 4,4 MB Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. |
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