### Integrability Theorems of Free Systems and Symplectic Haantjes Structures

Keiichi Kikuchi, Marin Drinov Academic Publishing House, Tsukasa Takeuchi
Published: 1 January 2022

Abstract: Ikeda and Sakamoto studied a dynamical control problem called the linear first integral for holonomic dynamical systems, and our proposition proved the same result as theirs in integrability. % Also, a symplectic Haantjes manifolds has been defined by Tempesta and Tondo, which is a characterization of integrable systems using $(1,1)$ tensor fields. We show integrability in dynamical control problems from a geometric point of view by means of a concrete construction of a symplectic Haantjes manifold.
Keywords: Structures / Haantjes / symplectic / proposition / Theorems / Sakamoto / concrete / Tempesta / Tondo / geometric

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