Homoclinic And Heteroclinic Orbits For A Class Of 4 Dimensional Hamiltonian Systems
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Homoclinic And Heteroclinic Orbits For A Class Of 4 Dimensional Hamiltonian Systems
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Author : Konstantin Michael Mischaikow
language : en
Publisher:
Release Date : 1985
Homoclinic And Heteroclinic Orbits For A Class Of 4 Dimensional Hamiltonian Systems written by Konstantin Michael Mischaikow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
A Study Of Heteroclinic Orbits For A Class Of Fourth Order Ordinary Differential Equations
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Author : Denis Bonheure
language : en
Publisher: Presses univ. de Louvain
Release Date : 2004
A Study Of Heteroclinic Orbits For A Class Of Fourth Order Ordinary Differential Equations written by Denis Bonheure and has been published by Presses univ. de Louvain this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
In qualitative theory of differential equations, an important role is played by special classes of solutions, like periodic solutions or solutions to some boundary value problems. When a system of ordinary differential equations has equilibria, i.e. constant solutions, whose stability properties are known, it is significant to search for connections between them by trajectories of solutions of the given system. These are called homoclinic or heteroclinic, according to whether they describe a loop based at one single equilibrium or they "start" and "end" at two distinct equilibria. This thesis is devoted to the study of heteroclinic solutions for a specific class of ordinary differential equations related to the Extended Fisher-Kolmogorov equation and the Swift-Hohenberg equation. These are semilinear fourth order bi-stable evolution equations which appear as mathematical models for problems arising in Mechanics, Chemistry and Biology. For such equations, the set of bounded stationary solutions is of great interest. These solve an autonomous fourth order equation. In this thesis, we focus on such equations having a variational structure. In that case, the solutions are critical points of an associated action functional defined in convenient functional spaces. We then look for heteroclinic solutions as minimizers of the action functional. Our main contributions concern existence and multiplicity results of such global and local minimizers in the case where the functional is defined from sign changing Lagrangians. The underlying idea is to impose conditions which imply a lower bound on the action over all admissible functions. We then combine classical arguments of the Calculus of Variations with careful estimates on minimizing sequences to prove the existence of a minimum.
Iutam Symposium On Dynamics And Control Of Nonlinear Systems With Uncertainty
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Author : H.Y. Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-26
Iutam Symposium On Dynamics And Control Of Nonlinear Systems With Uncertainty written by H.Y. Hu 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 2007-07-26 with Science categories.
This is a state-of-the-art treatise on the problems of both nonlinearity and uncertainty in the dynamics and control of engineering systems. The concept of dynamics and control implies the combination of dynamic analysis and control synthesis. It is essential to gain insight into the dynamics of a nonlinear system with uncertainty if any new control strategy is designed to utilize nonlinearity.
Dynamical Systems In Classical Mechanics
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Author : Valeriĭ Viktorovich Kozlov
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Dynamical Systems In Classical Mechanics written by Valeriĭ Viktorovich Kozlov 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 1995 with Mathematics categories.
This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include... the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics.
Hamiltonian Dynamics And Celestial Mechanics
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Author : Donald Saari
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Hamiltonian Dynamics And Celestial Mechanics written by Donald Saari 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 1996 with Mathematics categories.
The symbiotic of these two topics creates a natural combination for a conference on dynamics. Topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems.
Extended Abstracts Spring 2014
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Author : Montserrat Corbera
language : en
Publisher: Birkhäuser
Release Date : 2015-10-20
Extended Abstracts Spring 2014 written by Montserrat Corbera and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-20 with Mathematics categories.
The two parts of the present volume contain extended conference abstracts corresponding to selected talks given by participants at the "Conference on Hamiltonian Systems and Celestial Mechanics 2014" (HAMSYS2014) (15 abstracts) and at the "Workshop on Virus Dynamics and Evolution" (12 abstracts), both held at the Centre de Recerca Matemàtica (CRM) in Barcelona from June 2nd to 6th, 2014, and from June 23th to 27th, 2014, respectively. Most of them are brief articles, containing preliminary presentations of new results not yet published in regular research journals. The articles are the result of a direct collaboration between active researchers in the area after working in a dynamic and productive atmosphere. The first part is about Central Configurations, Periodic Orbits and Hamiltonian Systems with applications to Celestial Mechanics – a very modern and active field of research. The second part is dedicated to mathematical methods applied to viral dynamics and evolution. Mathematical modelling of biological evolution currently attracts the interest of both mathematicians and biologists. This material offers a variety of new exciting problems to mathematicians and reasonably inexpensive mathematical methods to evolutionary biologists. It will be of scientific interest to both communities. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.
Handbook Of Differential Equations Ordinary Differential Equations
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Author : A. Canada
language : en
Publisher: Elsevier
Release Date : 2006-08-21
Handbook Of Differential Equations Ordinary Differential Equations written by A. Canada and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-21 with Mathematics categories.
This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields
Hamiltonian Systems With Three Or More Degrees Of Freedom
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Author : Carles Simó
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hamiltonian Systems With Three Or More Degrees Of Freedom written by Carles Simó 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.
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.
Handbook Of Dynamical Systems
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Author : H. Broer
language : en
Publisher: Elsevier
Release Date : 2010-11-10
Handbook Of Dynamical Systems written by H. Broer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.
In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems
Mathematics Of Complexity And Dynamical Systems
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05
Mathematics Of Complexity And Dynamical Systems written by Robert A. Meyers 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 2011-10-05 with Mathematics categories.
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.