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Topic: Hamiltonian dynamics

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	Dynamics and self-consistent chaos in a mean field Hamiltonian model (Site not responding. Last check: 2007-11-06)
		The goal of this project is to study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and in the N approchs infinite kinetic limit (where N is the number of particles).
		We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.
		The existence of phase space coherent structures in large degrees-of-freedom Hamiltonian systems is in principle puzzling because coherence requires some degree of integrability, which one might expect to lose as the number of degrees of freedom increases.
	www.ornl.gov /sci/fed/Theory/csd/research/projects/scc/das.htm (276 words)

	Nonlinear Science FAQ (Site not responding. Last check: 2007-11-06)
		A dynamical system consists of an abstract phase space or state space, whose coordinates describe the dynamical state at any instant; and a dynamical rule which specifies the immediate future trend of all state variables, given only the present values of those same state variables.
		Dynamical systems are "deterministic" if there is a unique consequent to every state, and "stochastic" or "random" if there is more than one consequent chosen from some probability distribution (the "perfect" coin toss has two consequents with equal probability for each initial state).
		Hamiltonian systems (sometimes mistakenly identified with the notion of conservative systems) always have such pairs of variables, and so the phase space is even dimensional.
	www.faqs.org /faqs/sci/nonlinear-faq (11552 words)

	CDSNS Workshop on Hamiltonian Dynamics (Site not responding. Last check: 2007-11-06)
		We prove that, under some non degeneracy conditions, one can construct transition chains along any interval using, besides the usual whiskered tori, what we call secondary objects, that can be secondary tori or (un)stable manifolds of periodic orbits which appear in the gaps which are devoid of whiskered tori.
		One can start introducing some simplifications in the original model, neglecting a term in its Hamiltonian so that the problem is reduced to a priori unstable three time scale system; for such systems a general theory of Arnold diffusion can indeed be developed.
		Abstract: It is well known that resonant tori in an integrable Hamiltonian system tend to be destroyed under arbitrary generic perturbations and give rise to a resonance zone containing both stochastic under arbitrary generic perturbations and give rise to a resonance zone containing both stochastic trajectories and regular orbits.
	www.math.gatech.edu /cdsns/events/program.html (949 words)

	FULL MODULE DESCRIPTION (Site not responding. Last check: 2007-11-06)
		Aims: To develop the theory and methods of Hamiltonian Dynamics with emphasis on a geometrical approach.
		A student should be able to derive the Hamiltonian structure related to a given Lagrangian; work with symplectic transformations; identify simple symmetries and conservation laws; apply the Hamiltonian perturbation theory to problems related to simple satellite dynamics problems.
		Hamiltonian formulation of classical mechanics; symplectic geometry; canonical transformations; Hamiltonian flows, symmetries, conservation laws and Noether’s theorem, Liouville’s volume theorem.
	www.open.mis.surrey.ac.uk /misweb/modules/6834.htm (236 words)

	HAMILTONIAN DYNAMICS (Site not responding. Last check: 2007-11-06)
		It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.
		As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry.
		As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.
	www.worldscibooks.com /physics/3637.htm (158 words)

	Hamiltonian Dynamics, Variational Principles and Symplectic Invariants by Helmut H.W. Hofer
		There is a very intricate relationship between (dynamical systems) questions in Hamiltonian dynamics and (geometric) questions in symplectic geometry.
		For example, the problem of finding periodic orbits on a prescribed energy surface is closely related to the problem of designing an energy-efficient transport for open sets in phase space.
		Autonomous Hamiltonian flows are geodesics for this metric (but not the unique ones) and periodic orbits are related to conjugate points.
	www.ima.umn.edu /PI/abstracts/hofer1.html (323 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		The dynamics is not well-defined outside the constraint manifold and can be modified, as long as it remains unchanged on the manifold.
		The stabilizing effect of the extended Hamiltonian and of the Dirac brackets, respectively, shows not only in the lower absolute values of the errors but also in their growth.
		Perturbed Hamiltonian State Space Form If we restrict to regular systems with m imposed constraints Öff(q) = 0 where the Hamiltonian is separable and of the form H0(q; p) = 12 ptp + V (q), we can to some extent also perform part (B) of the stability analysis using again a perturbation approach.
	www.ubka.uni-karlsruhe.de /vvv/1997/informatik/9/9.text (8129 words)

	On Hamiltonian And Quantum Dynamics Of Massless Particles. (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: A short review of special relativistic dynamics describing a particle acted upon by an arbitrary conservative external force is presented.
		Hamiltonian flows on the twistor phase space T are constructed which, for conservative forces and value of the helicity equal to zero, reproduce equations of motion of the classical massless particle.
		1 Hamiltonian Dynamics of Massless Objects (context) - Bette - 1994
	citeseer.ist.psu.edu /110073.html (349 words)

	GEOMETRY AND DYNAMICS
		A classification of the heteroclinic cycles (including `pinched tori') that can occur as singular fibres of energy-momentum maps of Liouville integrable systems, and of the corresponding torus fibrations (with monodromy) over the complements of their discriminants.
		One of the aims of the network is to adapt and combine these with standard non-symmetric Hamiltonian methods to initiate a theory of Hamiltonian symmetric chaos.
		Return map techniques will be used to investigate the effects of monodromy on dynamics near perturbed pinched tori and more general heteroclinic cycles.
	www.ma.umist.ac.uk /jm/MASIE/projects/sec1.html (976 words)

	CHAOTIC DYNAMICS IN HAMILTONIAN SYSTEMS (Site not responding. Last check: 2007-11-06)
		This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research.
		It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM theory, the Melnikov method, and Arnold diffusion.
		Theoretical discussions are illustrated by a study of the dynamics of small circumasteroidal grains perturbed by solar radiation pressure.
	www.worldscibooks.com /chaos/3554.html (213 words)

	Science and Education Information book reviews - Classical Dynamics (Site not responding. Last check: 2007-11-06)
		Indeed, in Classical Dynamics topics like oscillations and gravitation are treated within the Newtonian framework, while Goldstein does it the Lagrangian/Hamiltonian way.
		If one does indeed recognize that Classical Dynamics has to be followed up by a more advanced education that has more to say about Lagrangian/Hamiltonian mechanics, then Classical Dynamics is a very fine book at it's level.
		Some people regards Classical Dynamics as an ancient text because the subject isn't approached geometrically, that is, in terms of Clifford algebra.
	science-education.info /classical-dynamics.php (668 words)

	MA2061 Lagrangian and Hamiltonian Dynamics
		This course is an introduction to the classical Lagrangian and Hamiltonian methods of analytical dynamics.
		To introduce the powerful methods of analytical dynamics, and to apply the theory to some important physical problems.
		The selection of topics chosen will provide a foundation for further study, and be sufficient for the solution of most problems in dynamics that the student will encounter elsewhere in the degree.
	www.mcs.le.ac.uk /Modules/MA-02-03/MA2061.html (173 words)

	Classical Dynamics (Site not responding. Last check: 2007-11-06)
		Later came the dynamics of La Grange and the dynamics of Hamilton.
		LaGrangian and Hamiltonian dynamics are the touchstones of non-classical dynamics: quantum mechanics, special relativity, and general relativity.
		With Hamiltonian dynamics you use generalized coordinates and generalized momentum.
	home.texoma.net /~f3meyer/clasdyn.htm (759 words)

	Biophysics & Statistical Physics Group: non-Hamiltonian molecular dynamics
		Although (Hamiltonian) molecular dynamics has proven to be a very useful tool, it has one basic restriction: It can in principle generate only equilibrium properties of the microcanonical ensemble.
		Although the mechanical consequences of this procedure might be straightforward, the implications on the statistical mechanics of the system are less evident.
		Currently the use of non-Hamiltonian dynamical systems to perform molecular dynamics simulations is becoming more or less standard.
	www.lce.hut.fi /research/polymer/nHmd.shtml (335 words)

	Hamiltonian dynamics of extended objects (Site not responding. Last check: 2007-11-06)
		We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity.
		The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described.
		The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler–Lagrange equations.
	stacks.iop.org /0264-9381/21/5563 (337 words)

	Some intriguing open problems in Hamiltonian dynamics
		In general, it should depend on the dynamical properties of the billiard obtained when the container is at rest.
		Call the "good set" the maximal invariant subset in the phase space of a Hamiltonian systems for which the invariant Liouville measure is almost periodic.
		Yes, the dynamics should exist for any smooth initial measure in the phase space and the motion is conjugated to an isospectral deformation of a Calderon-Zygmund operator.
	abel.math.harvard.edu /~knill/seminars/intr (1532 words)

	Dynamics Conferences
		It is meant for PhD students (or recent PhDs) in complex dynamics or related areas and it will consist of 3 mini courses of 5 hours each and student talks.
		The conference will provide a unique international forum for the international community of mathematicians and scientists working in analysis, differential equations, dynamical systems, and their applications to real world problems in the forms of modeling and computation.
		The aim of this conference is to bring together the worldwide senior experts and young researchers as well to this beautiful city, Poitiers, to report recent achievements, exchange ideas, and address future trends of research, in a relaxing and stimulating environment.
	www.math.sunysb.edu /dynamics/conferences/conferences.html (1787 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Its basic application is the classification of dynamical systems into categories by transforming nonlinear vector fields into a standard form which is determined by their linear part; one expects that the solution sets of those dynamical systems whose vector fields lie in the same category should exhibit similar features.
		The minimal model of Ca2+ dynamics is obtained via a systematic reduction of the biophysical model and its analytically obtained behaviour is shown to be in excellent agreement with the original biophysical model.
		Members of the worldwide scientific, medical and engineering communities interested in recent developments and techniques of experimental nonlinear dynamics are invited to attend the conference and to contribute to its technical sessions and workshops.
	www.agnld.uni-potsdam.de /~shw/events/uk-nonl-subs2004-02.txt (8898 words)

	OUP: Hamiltonian Chaos and Fractional Dynamics: Zaslavsky
		The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology.
		The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others.
		An understanding of the origin of randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry, and engineering.
	www.oup.co.uk /isbn/0-19-852604-0 (485 words)

	Course on Chaotic Hamiltonian Dynamics (Site not responding. Last check: 2007-11-06)
		Three dimensional dynamics: the Lorenz attractor and Shilnikov's mechanism for chaos.
		Meyer, K. and Hall, "Introduction to Hamiltonian dynamical systems and the N-body problem", Springer-Verlag, New York, 1992.
		Guckenheimer, J and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Guckenheimer, J and P. Holmes, Springer-Verlag, 1983.
	www.wisdom.weizmann.ac.il /~vered/course03.html (400 words)

	Integrable and nonintegrable behavior in Hamiltonian dynamics (Site not responding. Last check: 2007-11-06)
		After an introduction for students, where I'll present briefly how these systems appear in mechanics and mathematics, and what are their very elementary properties distinguishing them among general smooth dynamical systems, I'll present an approach to the study of integrable Hamiltonian systems giving a principal that allows us to understand their phase space structure.
		The second part of the talk will be devoted to the dynamics of nonintegrable Hamiltonian systems.
		Since the topic is too vast, I'll restrict myself on some elements of the orbit behavior for such systems near homoclinic orbits to equilibria to emphasize the distinction between integrable and nonintegrable systems, some criteria of nonintegrability, like the Melnikov method and so forth, will be shown.
	amath.colorado.edu /seminars/2004fall/Abstracts/Lerman.html (152 words)

	CIPS Directory - James E. Howard (Site not responding. Last check: 2007-11-06)
		My research interests lie mainly in applications of Hamiltonian dynamics to a wide variety of physical problems, including dust dynamics, asteroidal satellites, microwave ionization of Rydberg atoms, and RF ion traps.
		In addition I collaborate with Applied Mathematics faculty on dynamics problems and Aerospace Engineering faculty on sonic-boom simulations.
		I also work in such areas as nearly axisymmetric systems, martian dust-rings and the epicyclic motion of saturnian dust-grains, asteroidal satellites, as well as the stability of extrasolar planets around binary stars.
	www-plasma.colorado.edu /CIPSsite/profiles/profilehoward.html (213 words)

	Who Is Who Handbook of Nonlinear Dynamics
		Dynamics of solitons with applications in Solid State Physics and Nonlinear Electrical Transmission Lines - Nonlinear oscillations and chaos with applications in mechanical and electromechanical e (1)
		Stochastic and deterministic nonlinear dynamics of biological (1)
		the nonexistence of analytical integrals in dynamics; the Poisson's structure and the Lie algebras in Hamiltonian mechanics; the Kowalewsky method and the conditions of integrability;the dynamics in c (1)
	www.chaos-gruppe.de /wiw/subj.html (2464 words)

	SYNODE References
		Huang: A Hamiltonian approximation to simulate solitary waves of the Korteweg-de Vries equation, Math.
		Iserles: Stability and dynamics of numerical methods for ordinary differential equations, IMA J. Numer.
		Leimkuhler, S. Reich, and R. Skeel: Integration methods for molecular dynamics, In Jill P. Mesirov, Klaus Schulten, and De Witt Sumners, editors, Mathematical Approaches to Biomolecular Structure and Dynamics, volume 82 of IMA Volumes in Mathematics and its Applications.
	www.math.ntnu.no /num/synode/bib/hamilt/hamilt.html (6256 words)

	Derivation of Brownian motions from Hamiltonian dynamics with applications to SPDE (Site not responding. Last check: 2007-11-06)
		Derivation of Brownian motions from Hamiltonian dynamics with applications to SPDE
		Stochastic ordinary differential equations (SODE's) are derived from the deterministic dynamics of Hamiltonian systems of two types of particles, namely "big" and "small" particles.
		The number of big particles is finite and originally they have a spatial extension and are represented as balls.
	www.science.unitn.it /~tubaro/TeX/lavoro/kotelenez/node1.html (197 words)

	Model reference control using sliding mode with Hamiltonian dynamics (Site not responding. Last check: 2007-11-06)
		Sliding mode techniques largely simplify the task of tracking the reference model and are capable of accommodating the uncertainties present in the dynamics of the system.
		In this paper we are concerned with model tracking in finite time for plant and reference model which are given in Hamiltonian format.
		We also include the addition of a stabilising supervisory controller in terms of the Hamiltonian of the reference model.
	anziamj.austms.org.au /V45/E056/home.html (167 words)

	Course on Chaotic Hamiltonian Dynamics (Site not responding. Last check: 2007-11-06)
		March 21: linear Hamiltonian systems, symplectic and Hamiltonian matrices.
		March 28: Lagrangian splitting, spectrum of Hamiltonian matrices.
		April 23 (Monday!) Smale-Birkhoff homolinic theorem, Smale horseshoe and symbolic dynamics.
	www.wisdom.weizmann.ac.il /~vered/course01.html (338 words)

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