Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems

@article{HernndezBermejo2008GeneralizationOS,
  title={Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems},
  author={Benito Hern{\'a}ndez-Bermejo},
  journal={Journal of Mathematical Analysis and Applications},
  year={2008},
  volume={344},
  pages={655-666}
}
  • B. Hernández-Bermejo
  • Published 15 August 2008
  • Mathematics
  • Journal of Mathematical Analysis and Applications

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References

SHOWING 1-10 OF 46 REFERENCES

New solution family of the Jacobi equations: Characterization, invariants, and global Darboux analysis

A new family of skew-symmetric solutions of the Jacobi partial differential equations for finite-dimensional Poisson systems is characterized and analyzed. Such family has some remarkable properties.

New solutions of the Jacobi equations for three-dimensional Poisson structures

A systematic investigation of the skew-symmetric solutions of the three-dimensional Jacobi equations is presented. As a result, three disjoint and complementary new families of solutions are

Hamiltonian structure and Darboux theorem for families of generalized Lotka–Volterra systems

This work is devoted to the establishment of a Poisson structure for a format of equations known as generalized Lotka–Volterra systems. These equations, which include the classical Lotka–Volterra

Poisson structure of dynamical systems with three degrees of freedom

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one‐form in three dimensions. Advantage is taken of this fact and

Multiple lie-poisson structures, reductions, and geometric phases for the Maxwell-Bloch travelling wave equations

SummaryThe real-valued Maxwell-Bloch equations on ℝ3 are investigated as a Hamiltonian dynamical system obtained by applying an S1 reduction to an invariant subsystem of a dynamical system on ℂ3.

Bi-Hamiltonian systems of deformation type

Characterization, global analysis and integrability of a family of Poisson structures

Quasi-Hamiltonian Structure and Hojman Construction

The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system

A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result.

Nonlinear stability of fluid and plasma equilibria