Bihamilon structure and singularities of momentum mapping for Lagrange top

We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The spectral sequence converges to the Poisson cohomology of the manifold and has the E2-term equal to the tensor product of the cohomology of the Lie algebra and the equivariant Poisson cohomology of the manifold. The latter is defined as the equivariant cohomology of the multi-vector fields made into a G-differential complex by means of the momentum mapping. An extensive introduction to equivariant cohomology of G-differential complexes is given including some new results and a number of examples and applications are considered.

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Spin-to-Orbital Angular Momentum Mapping of Polychromatic Light

Physical Review Letters ◽

10.1103/physrevlett.120.213903 ◽

2018 ◽

Vol 120 (21) ◽

Cited By ~ 14

Author(s):

Mushegh Rafayelyan ◽

Etienne Brasselet

Keyword(s):

Angular Momentum ◽

Orbital Angular Momentum ◽

Momentum Mapping ◽

Polychromatic Light

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Position and momentum mapping of vibrations in graphene nanostructures

Nature ◽

10.1038/s41586-019-1477-8 ◽

2019 ◽

Vol 573 (7773) ◽

pp. 247-250 ◽

Cited By ~ 20

Author(s):

Ryosuke Senga ◽

Kazu Suenaga ◽

Paolo Barone ◽

Shigeyuki Morishita ◽

Francesco Mauri ◽

...

Keyword(s):

Momentum Mapping ◽

Graphene Nanostructures

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THE 2-D SEXTIC HAMILTONIAN OSCILLATOR

International Journal of Bifurcation and Chaos ◽

10.1142/s021812741330019x ◽

2013 ◽

Vol 23 (06) ◽

pp. 1330019

Author(s):

F. J. MOLERO ◽

J. C. VAN DER MEER ◽

S. FERRER ◽

F. J. CÉSPEDES

Keyword(s):

Phase Space ◽

Elliptic Functions ◽

Singular Values ◽

Nonlinear Oscillators ◽

Momentum Mapping ◽

Dimensional Model ◽

Integrable Hamiltonian Systems ◽

One Dimensional ◽

Dimensional Phase Space ◽

The One

The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundamental fibration of the four-dimensional phase space. Special attention is given to the singular values of the energy-momentum mapping connected with rectilinear and circular orbits. They are related to the saddle-center and pitchfork scenarios with the associated homoclinic and heteroclinic trajectories. We also study how the geometry of the phase space evolves during the transition from the one-dimensional to the two-dimensional model. Within an elliptic function approach, the solutions are given using Legendre elliptic integrals of the first and third kind and the corresponding Jacobi elliptic functions.

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