# 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…

## 4 Citations

A pr 2 02 1 3 D-flows Generated by the Curl of a Vector Potential

- Mathematics
- 2021

We examine 3D flows ẋ = v(x) admitting vector identity Mv = ∇×A for a multiplier M and a potential field A. It is established that, for those systems, one can complete the vector field v into a basis…

On the quest for generalized Hamiltonian descriptions of 3D-flows generated by the curl of a vector potential

- Computer ScienceInternational Journal of Geometric Methods in Modern Physics
- 2020

This work examines Hamiltonian analysis of three-dimensional advection flow of incompressible nature and elaborate Nambu–Hamiltonian and bi-Hamiltonian characters of such systems under the light of vanishing or non-vanishing of the quantity.

N ov 2 01 5 Bi-Hamiltonian Structures of Chaotic Dynamical Systems in 3 D

- 2015

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