Superintegrable Cases of Four Dimensional Dynamical Systems
O\u{g}ul Esen, Anindya Ghose Choudhury, Partha Guha, Hasan G\"umral
TL;DR
This paper identifies superintegrable cases in four-dimensional dynamical systems, specifically hyperchaotic L"{u} and Qi systems, by demonstrating their tri-Hamiltonian structures at specific parameter values.
Contribution
It reveals new superintegrable instances of hyperchaotic systems and establishes their tri-Hamiltonian structures, expanding understanding of integrability in high-dimensional systems.
Findings
Hyperchaotic L"{u} and Qi systems are superintegrable at specific parameters.
These systems admit tri-Hamiltonian structures.
Degenerate tri-Hamiltonian structures are exhibited for certain equations.
Abstract
Degenerate tri-Hamiltonian structures of Shivamoggi and generalized Raychaudhuri equations are exhibited. For certain specific values of the parameters, it is shown that hyperchaotic L\"{u} and Qi systems are superintegrable and admit tri-Hamiltonian structures.
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