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math.DS2025
Geometric Dynamical Systems
Ghorbanali Haghighatdoost
This article provides a conceptual and historical review of the evolution of integrable Hamiltonian systems from the Moscow School of A. T. Fomenko to the emerging Azarbaijan Schoo…
math.DS2025
Euler Poincare Dynamics and Control on Lie Groupoids
Ghorbanali Haghighatdoost
We extend the Euler Poincare formalism from Lie groups to Lie groupoids for optimal control problems. While Lie algebroids provide the standard infinitesimal framework, the groupoi…
math.DS2024
A note on integrabiliy of Hamiltonian systems on the co-adjoint Lie groupoids
Ghorbanali Haghighatdoost, Rezvaneh Ayoubi
As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy…