• Corpus ID: 115177289

Existence of Hamiltonian Structure in 3D

@inproceedings{Gumral2010ExistenceOH,
  title={Existence of Hamiltonian Structure in 3D},
  author={Hasan Gumral},
  year={2010}
}
In three dimensions, the construction of bi-Hamiltonian structure can be reduced to the solutions of a Riccati equation with the arclength coordinate of a Frenet-Serret frame being the independent variable. Explicit integration of conserved quantities are connected with the coefficients of Riccati equation which are elements of the third cohomology class. All explicitly constructed examples of bi-Hamiltonian systems are exhausted when this class along with the first one vanishes. The latter… 
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References

SHOWING 1-10 OF 51 REFERENCES
Bi-Hamiltonian structure in Frenet–Serret frame
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
Integrals of motion for three-dimensional non-Hamiltonian dynamical systems
The problem of finding integrals of motion of three-dimensional dynamical systems is analysed. The authors introduce a new type of direct method in the search of parameter values for which an
A time-extended Hamiltonian formalism
Hamiltonian equations in R 3
is shown to be valid also in the neighborhood of some irregular points. Compatible Poisson structures and corresponding bi-Hamiltonian systems are also discussed. Hamiltonian structures, the
Generalized Hamiltonian dynamics
Taking the Liouville theorem as a guiding principle, we propose a possible generalization of classical Hamiltonian dynamics to a three-dimensional phase space. The equation of motion involves two
A Simple model of the integrable Hamiltonian equation
A method of analysis of the infinite‐dimensional Hamiltonian equations which avoids the introduction of the Backlund transformation or the use of the Lax equation is suggested. This analysis is based
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
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