Bi-Hamiltonian Structures of Chaotic Dynamical Systems in 3D

Abstract

We study Poisson structures of dynamical systems with three degrees of freedom which are known for their chaotic properties, namely Lü, modified Lü, Chen, $T$ and Qi systems. We show that all these flows admit bi-Hamiltonian structures depending on the values of their parameters.

14 pages

References in corpus (5)

• Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems
• New solutions of the Jacobi equations for three-dimensional Poisson structures
• One solution of the 3D Jacobi identities allows determining an infinity of them
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Cited by in corpus (3)

• On Time-dependent Hamiltonian Realizations of Planar and Nonplanar Systems
• On the quest for generalized Hamiltonian descriptions of $3D$-flows generated by curl of a vector potential
• On novel Hamiltonian descriptions of some three-dimensional non-conservative systems