Download or read book Seeking Stability in Hamiltonian Systems with Two Degrees of Freedom written by Mark Francis Demers and published by . This book was released on 1994 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Formal Stability of Hamiltonian Systems with Two Degrees of Freedom written by Stephen P. Diliberto and published by . This book was released on 1966 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motion near periodic solutions is characterized by the eigen-values of the linear terms of the differential equation in local coordinates. When these local coordinates have purely imaginary characteristic roots the possibility of stability exists. When these roots are commensurable with the frequency of the periodic solution the system is in general unstable. It was believed that there were an infinite set of algebraic conditions necessary for formal stability. These are herein to reduce to two for a Hamiltonian system with two degrees of freedom. (Author).
Download or read book Stability of the Equilibrium Points in Hamiltonian Systems written by I︠U︡. S. Ilʹi︠a︡shenko and published by . This book was released on 1990 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability of the equilibrium points in Hamiltonian systems with two degrees of freedom written by Julij S. Ilʹjašenko and published by . This book was released on 1990 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability of the Equilibrium Points in Hamiltonian Systems with Two Degrees of Freedom written by Ju. S. Il'yashenko and published by . This book was released on 1990 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Investigation of the Stability of Three Degree of Freedom Hamiltonian Systems in Presence of a Third Order Resonance written by David Louis Richardson and published by . This book was released on 1972 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Normal Forms and Stability of Hamiltonian Systems written by Hildeberto E. Cabral and published by Springer Nature. This book was released on 2023-09-12 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics. This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems. With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.
Download or read book Complex Hamiltonian Dynamics written by Tassos Bountis and published by Springer Science & Business Media. This book was released on 2012-04-03 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores modern developments in Hamiltonian dynamical systems, focusing on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. Includes end-of-chapter exercises and challenging problems.
Download or read book Some Remarks on Integrable Hamiltonian Systems with Two Degrees of Freedom written by Nguyen Tien Dung and published by . This book was released on 1993 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Integrability and Nonintegrability of Hamiltonian Systems with Two Degrees of Freedom written by Vyacheslav V. Stepanov and published by . This book was released on 1999 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Chaotic Transport in Dynamical Systems written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. Illustrating phase space transport problems arising in a variety of applications that can be modeled as time-periodic perturbations of planar Hamiltonian systems, the book begins with the study of transport in the associated two-dimensional Poincaré Map. This serves as a starting point for the further motivation of the transport issues through the development of ideas in a non-perturbative framework with generalizations to higher dimensions as well as more general time dependence. A timely and important contribution to those concerned with the applications of mathematics.
Download or read book Lectures on Hamiltonian Systems written by Jürgen Moser and published by American Mathematical Soc.. This book was released on 1968 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hamiltonian Systems with Three or More Degrees of Freedom written by Carles Simó and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.
Download or read book Metamorphoses of Hamiltonian Systems with Symmetries written by Konstantinos Efstathiou and published by Springer. This book was released on 2005-01-28 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hamiltonian Dynamical Systems written by R.S MacKay and published by CRC Press. This book was released on 2020-08-18 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.
Download or read book Hamiltonian Mechanics written by John Seimenis and published by NATO Science Series B. This book was released on 1994-12-31 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents papers from the first scientific conference in Eastern Europe supported by NATO. Topics include chaos theory, periodic solutions of nonlinear Schrodinger equations and the Nash-Moser method, adiabatic invariants, exponentially small splitting in Hamiltonian systems, and the dynamics of trace maps.
Download or read book Notes on Hamiltonian Dynamical Systems Notes on Hamiltonian Dynamical Systems written by Antonio Giorgilli and published by Cambridge University Press. This book was released on 2022-05-05 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov–Arnold–Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.
