# 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} }

## 14 Citations

### Congruence method for global Darboux reduction of finite-dimensional Poisson systems

- MathematicsJournal of Mathematical Physics
- 2018

A new procedure for the global construction of the Casimir invariants and Darboux canonical form for finite-dimensional Poisson systems is developed. This approach is based on the concept of matrix…

### Inverse Jacobi multiplier as a link between conservative systems and Poisson structures

- Mathematics
- 2017

Some aspects of the relationship between conservativeness of a dynamical system (namely the preservation of a finite measure) and the existence of a Poisson structure for that system are analyzed.…

### Poisson systems as the natural framework for additional first integrals via Darboux invariant hypersurfaces

- Mathematics
- 2013

### Poisson Brackets after Jacobi and Plücker

- MathematicsRegular and Chaotic Dynamics
- 2018

We construct a symplectic realization and a bi-Hamiltonian formulation of a 3-dimensional system whose solution are the Jacobi elliptic functions. We generalize this system and the related Poisson…

### Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems

- Mathematics
- 2011

### Perturbed rank 2 Poisson systems and periodic orbits on Casimir invariant manifolds

- Mathematics
- 2020

A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be…

### A stability criterion for non-degenerate equilibrium states of completely integrable systems

- Mathematics
- 2016

### Numerical methods preserving multiple Hamiltonians for stochastic Poisson systems

- Mathematics, Computer ScienceDiscrete & Continuous Dynamical Systems - S
- 2021

This paper proposes a class of numerical schemes for stochastic Poisson systems with multiple invariant Hamiltonians based on the average vector field discrete gradient and an orthogonal projection technique and proves that these schemes preserve the Casimir functions of the systems under certain conditions.

## References

SHOWING 1-10 OF 46 REFERENCES

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

- Mathematics
- 2007

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

- Mathematics
- 2001

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

- Mathematics
- 1998

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

- Mathematics
- 1993

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

- Mathematics
- 1992

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.…

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

- Mathematics
- 2008

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

- Mathematics, Physics
- 1996

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.…