Integrability Theorems of Free Systems and Symplectic Haantjes Structures

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.