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| Author | : Maciej Blaszak |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 355 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 364258893X |
Download Multi-Hamiltonian Theory of Dynamical Systems Book in PDF, ePub and Kindle
This book offers a modern introduction to the Hamiltonian theory of dynamical systems, presenting a unified treatment of all types of dynamical systems, i.e., finite, lattice, and field. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system. As this property is closely related to integrability, this book presents an algebraic theory of integrable.
| Author | : Maciej Błaszak |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 368 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : |
Download Multi-Hamiltonian Theory of Dynamical Systems Book in PDF, ePub and Kindle
This book offers a modern introduction to the Hamiltonian theory of dynamical systems, presenting a unified treatment of all types of dynamical systems, i.e., finite, lattice, and field. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system.
| Author | : Kenneth R. Meyer |
| Publisher | : Springer |
| Total Pages | : 389 |
| Release | : 2017-05-04 |
| Genre | : Mathematics |
| ISBN | : 3319536915 |
Download Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Book in PDF, ePub and Kindle
This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)
| Author | : Walter Craig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 450 |
| Release | : 2008-02-17 |
| Genre | : Mathematics |
| ISBN | : 1402069642 |
Download Hamiltonian Dynamical Systems and Applications Book in PDF, ePub and Kindle
This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
| Author | : Kenneth Meyer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2008-12-05 |
| Genre | : Mathematics |
| ISBN | : 0387097244 |
Download Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Book in PDF, ePub and Kindle
Arising from a graduate course taught to math and engineering students, this text provides a systematic grounding in the theory of Hamiltonian systems, as well as introducing the theory of integrals and reduction. A number of other topics are covered too.
| Author | : H.S. Dumas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 392 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461384486 |
Download Hamiltonian Dynamical Systems Book in PDF, ePub and Kindle
From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.
| Author | : Eduard Zehnder |
| Publisher | : European Mathematical Society |
| Total Pages | : 372 |
| Release | : 2010 |
| Genre | : Dynamics |
| ISBN | : 9783037190814 |
Download Lectures on Dynamical Systems Book in PDF, ePub and Kindle
This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smale's theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum. The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed. There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology.
| Author | : Antonio Giorgilli |
| Publisher | : Cambridge University Press |
| Total Pages | : 473 |
| Release | : 2022-05-05 |
| Genre | : Science |
| ISBN | : 1009151142 |
Download Notes on Hamiltonian Dynamical Systems Book in PDF, ePub and Kindle
Introduces Hamiltonian dynamics from the very beginning, culminating in the most important recent results: Kolmogorov's and Nekhoroshev's.
| Author | : G. Fusco |
| Publisher | : Elsevier |
| Total Pages | : 278 |
| Release | : 2016-06-03 |
| Genre | : Mathematics |
| ISBN | : 1483217892 |
Download Advanced Topics in the Theory of Dynamical Systems Book in PDF, ePub and Kindle
Advanced Topics in the Theory of Dynamical Systems covers the proceedings of the international conference by the same title, held at Villa Madruzzo, Trento, Italy on June 1-6, 1987. The conference reviews research advances in the field of dynamical systems. This book is composed of 20 chapters that explore the theoretical aspects and problems arising from applications of these systems. Considerable chapters are devoted to finite dimensional systems, with special emphasis on the analysis of existence of periodic solutions to Hamiltonian systems. Other chapters deal with infinite dimensional systems and the developments of methods in the general approach to existence and qualitative analysis problems in the general theory, as well as in the study of particular systems concerning natural sciences. The final chapters discuss the properties of hyperbolic sets, equivalent period doubling, Cauchy problems, and quasiperiodic solitons for nonlinear Klein-Gordon equations. This book is of value to mathematicians, physicists, researchers, and advance students.
| Author | : Johan Dubbeldam |
| Publisher | : John Wiley & Sons |
| Total Pages | : 261 |
| Release | : 2011-02-21 |
| Genre | : Science |
| ISBN | : 3527409319 |
Download The Complexity of Dynamical Systems Book in PDF, ePub and Kindle
Written by recognized experts, this edited book covers recent theoretical, experimental and applied issues in the growing fi eld of Complex Systems and Nonlinear Dynamics. It is divided into two parts, with the first section application based, incorporating the theory of bifurcation analysis, numerical computations of instabilities in dynamical systems and discussing experimental developments. The second part covers the broad category of statistical mechanics and dynamical systems. Several novel exciting theoretical and mathematical insights and their consequences are conveyed to the reader.
