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Symmetries and currents in nonholonomic mechanics

Michal Čech, Jana Musilová (2014)

Communications in Mathematics

In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical theory...

Symmetries in finite order variational sequences

Mauro Francaviglia, Marcella Palese, Raffaele Vitolo (2002)

Czechoslovak Mathematical Journal

We refer to Krupka’s variational sequence, i.e. the quotient of the de Rham sequence on a finite order jet space with respect to a ‘variationally trivial’ subsequence. Among the morphisms of the variational sequence there are the Euler-Lagrange operator and the Helmholtz operator. In this note we show that the Lie derivative operator passes to the quotient in the variational sequence. Then we define the variational Lie derivative as an operator on the sheaves of the variational sequence. Explicit...

Symmetries of connections on fibered manifolds

Alexandr Vondra (1994)

Archivum Mathematicum

The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.

Symmetry of local minimizers for the three-dimensional Ginzburg–Landau functional

Vincent Millot, Adriano Pisante (2010)

Journal of the European Mathematical Society

We classify nonconstant entire local minimizers of the standard Ginzburg–Landau functional for maps in H loc 1 ( ℝ 3 ; ℝ 3 ) satisfying a natural energy bound. Up to translations and rotations,such solutions of the Ginzburg–Landau system are given by an explicit solution equivariant under the action of the orthogonal group.

Symplectic classification of parametric complex plane curves

Goo Ishikawa, Stanisław Janeczko (2010)

Annales Polonici Mathematici

Based on the discovery that the δ-invariant is the symplectic codimension of a parametric plane curve singularity, we classify the simple and uni-modal singularities of parametric plane curves under symplectic equivalence. A new symplectic deformation theory of curve singularities is established, and the corresponding cyclic symplectic moduli spaces are reconstructed as canonical ambient spaces for the diffeomorphism moduli spaces which are no longer Hausdorff spaces.

Currently displaying 501 – 520 of 535