A double chain of coupled circuits in analogy with mechanical lattices.
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A new Lagrangian dynamic reduction in field theory
François Gay-Balmaz, Tudor S. Ratiu (2010)
Annales de l’institut Fourier
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.
A survey on Nambu-Poisson brackets.
Vaisman, I. (1999)
Acta Mathematica Universitatis Comenianae. New Series
Algèbres de Lie, systèmes hamiltoniens, courbes algébriques
Jean-Louis Verdier (1980/1981)
Séminaire Bourbaki
Canonical formulation of newtonian dynamics
J. Śniatycki, W. M. Tulczyjew (1972)
Annales de l'I.H.P. Physique théorique
Comment by the editors on the paper : “The hamiltonian formalism in higher order variational problems”
M. Francaviglia, D. Krupka (1985)
Annales de l'I.H.P. Physique théorique
Critical diffusions
Edward Nelson (1985)
Séminaire de probabilités de Strasbourg
Critical Point Theorems for Indefinite Functionals.
Vieri Benci, Paul H. Rabinowitz (1979)
Inventiones mathematicae
Dirac brackets in geometric dynamics
Jedrzej Śniatycki (1974)
Annales de l'I.H.P. Physique théorique
Erratum : “On the geometry of subbundles and Lagrange foliations”
P. Dazord (1985)
Annales scientifiques de l'École Normale Supérieure
Erratum : “The quantum stability problem for time-periodic perturbations of the harmonic oscillator”
M. Combescure (1987)
Annales de l'I.H.P. Physique théorique
Fundamental vector fields on type fibres of jet prolongations of tensor bundles
Demeter Krupka (1979)
Mathematica Slovaca
Nambu-Lie group actions.
Ciccoli, N. (2001)
Acta Mathematica Universitatis Comenianae. New Series
New trends in mechanics. I. Generalized differential variational principles in rational mechanics.
D. Mangeron, N. Irimiciuc, U. D'Ambrosio (1981)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
Normal Modes for Nonlinear Hamiltonian Systems.
Alan Weinstein (1973)
Inventiones mathematicae
On a horizontal structure on differentiable manifolds
Anton Dekrét (1977)
Mathematica Slovaca
On a Trace Functional for Formal Pseudo-Differential Operators and the Symplectic Structure of the Korteweg-Devries Type Equation.
M. Adler (1978/1979)
Inventiones mathematicae
On decomposability of Nambu-Poisson tensor.
Alekseevsky, D., Guha, P. (1996)
Acta Mathematica Universitatis Comenianae. New Series
On the algebraic structure on the jet prolongations of fibred manifolds
Ivan Kolář, Marco Modugno (1990)
Czechoslovak Mathematical Journal
Poincaré-Cartan forms in higher order variational calculus on fibred manifolds.
Jaime Muñoz Masqué (1985)
Revista Matemática Iberoamericana
The aim of the present work is to present a geometric formulation of higher order variational problems on arbitrary fibred manifolds. The problems of Engineering and Mathematical Physics whose natural formulation requires the use of second order differential invariants are classic, but it has been the recent advances in the theory of integrable non-linear partial differential equations and the consideration in Geometry of invariants of increasingly higher orders that has highlighted the interest...
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