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Bifurcations In Hamiltonian Systems
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Book Synopsis Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems by : Heinz Hanßmann
Download or read book Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems written by Heinz Hanßmann and published by Springer. This book was released on 2006-10-18 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
Book Synopsis Bifurcations in Hamiltonian Systems by : Henk Broer
Download or read book Bifurcations in Hamiltonian Systems written by Henk Broer and published by Springer. This book was released on 2003-01-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.
Book Synopsis Bifurcations in Hamiltonian Systems by : Henk Broer
Download or read book Bifurcations in Hamiltonian Systems written by Henk Broer and published by . This book was released on 2014-01-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Hamiltonian Hopf Bifurcation by : Jan Cornelis van der Meer
Download or read book The Hamiltonian Hopf Bifurcation written by Jan Cornelis van der Meer and published by Springer. This book was released on 2006-11-14 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bifurcations in Hamiltonian Systems by : Gerard Anton Lunter
Download or read book Bifurcations in Hamiltonian Systems written by Gerard Anton Lunter and published by . This book was released on 1999 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamics, Bifurcations and Control by : Fritz Colonius
Download or read book Dynamics, Bifurcations and Control written by Fritz Colonius and published by Springer. This book was released on 2003-07-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume originates from the Third Nonlinear Control Workshop "- namics, Bifurcations and Control", held in Kloster Irsee, April 1-3 2001. As the preceding workshops held in Paris (2000) and in Ghent (1999), it was organized within the framework of Nonlinear Control Network funded by the European Union (http://www.supelec.fr/lss/NCN). The papers in this volume center around those control problems where phenomena and methods from dynamical systems theory play a dominant role. Despite the large variety of techniques and methods present in the c- tributions, a rough subdivision can be given into three areas: Bifurcation problems, stabilization and robustness, and global dynamics of control s- tems. A large part of the fascination in nonlinear control stems from the fact that is deeply rooted in engineering and mathematics alike. The contributions to this volume reflect this double nature of nonlinear control. We would like to take this opportunity to thank all the contributors and the referees for their careful work. Furthermore, it is our pleasure to thank Franchise Lamnabhi-Lagarrigue, the coordinator of our network, for her s- port in organizing the workshop and the proceedings and for the tremendous efforts she puts into this network bringing the cooperation between the d- ferent groups to a new level. In particular, the exchange and the active p- ticipation of young scientists, also reflected in the Pedagogical Schools within the Network, is an asset for the field of nonlinear control.
Book Synopsis Dynamics, Bifurcation and Symmetry by : Pascal Chossat
Download or read book Dynamics, Bifurcation and Symmetry written by Pascal Chossat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc cess of this conference.
Book Synopsis Bifurcation of Periodic Orbits of Nonpositive Definite Hamiltonian Systems by : Yŏng-in Kim
Download or read book Bifurcation of Periodic Orbits of Nonpositive Definite Hamiltonian Systems written by Yŏng-in Kim and published by . This book was released on 1986 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bifurcations in Hamiltonian Systems by : Gerard Anton Lunter
Download or read book Bifurcations in Hamiltonian Systems written by Gerard Anton Lunter and published by . This book was released on 1999 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Metamorphoses of Hamiltonian Systems with Symmetries by : Konstantinos Efstathiou
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.
Book Synopsis Bifurcations Into Pathology for Hamiltonian Systems by : Konstantin Mischaikow
Download or read book Bifurcations Into Pathology for Hamiltonian Systems written by Konstantin Mischaikow and published by . This book was released on 1986 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a geometric analysis of bifurcations leading to chaos for Hamiltonian systems with two degrees of freedom of the form x-dot = y, y-dot = -gradient V(x). Two bifurcation parameters are considered. One is the energy level and the other is an angle, Psi, between two homoclinic orbits. Though global non-linearities are necessary, the results are obtained by local analysis of the flow near the origin where it is assumed that (D-sq)V(0) = I, the 2 x 2 identity matrix. For a fixed energy level it is shown that as Psi decreases through 90 deg the two homoclinic orbits bifurcate into two homoclinic orbits, a periodic orbit, and connecting orbits. These orbits can then be used to define a compact region in R supercript 4. Now treating the energy as a parameter value the trajectory of orbits passing through this compact region can be described using symbolic dynamics. In this case it is shown that a single periodic orbit bifurcates into three periodic orbits whose stable and unstable manifold intersect transversely.
Author :Konstantinos Efstathiou Publisher :Springer Science & Business Media ISBN 13 :9783540243168 Total Pages :164 pages Book Rating :4.2/5 (431 download)
Book Synopsis Metamorphoses of Hamiltonian Systems with Symmetries by : Konstantinos Efstathiou
Download or read book Metamorphoses of Hamiltonian Systems with Symmetries written by Konstantinos Efstathiou and published by Springer Science & Business Media. This book was released on 2005 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Resonance And Bifurcation To Chaos In Pendulum by : Albert C J Luo
Download or read book Resonance And Bifurcation To Chaos In Pendulum written by Albert C J Luo and published by World Scientific. This book was released on 2017-12-15 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system.This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum.
Book Synopsis Bifurcations from Relative Equilibria of Hamiltonian Systems by : R. M. Roberts
Download or read book Bifurcations from Relative Equilibria of Hamiltonian Systems written by R. M. Roberts and published by . This book was released on 1996 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Equations and Control Theory by : Z. Deng
Download or read book Differential Equations and Control Theory written by Z. Deng and published by CRC Press. This book was released on 2020-11-25 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the proceedings from the International Conference on Differential Equations and Control Theory, held recently in Wuhan, China. It provides an overview of current developments in a range of topics including dynamical systems, optimal control theory, stochastic control, chaos, fractals, wavelets and ordinary, partial, functional and stochastic differential equations.
Book Synopsis Generic Bifurcation of Hamiltonian Systems with Symmetry by : Martin Golubitsky
Download or read book Generic Bifurcation of Hamiltonian Systems with Symmetry written by Martin Golubitsky and published by . This book was released on 1986 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bifurcations of Periodic Orbits in Hamiltonian Systems with Symmetries by : Holger Lars Then
Download or read book Bifurcations of Periodic Orbits in Hamiltonian Systems with Symmetries written by Holger Lars Then and published by . This book was released on 1999 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
