Dynamical Symmetries for Graded Vector Fields. Issue 2 (3rd July 2019)

• Record Type: Journal Article
• Authors: Azizpour, Esmaeil; Atayi, Dordi Mohammad
• Is Part Of: Journal of dynamical systems and geometric theories. Volume 17:Issue 2(2019)
• Page Start: 187
• Page End: 203
• Publication Date: 2019-07-03
• Subjects: 58A50 -- 58A30 -- 58C50 -- 70H33; supermanifold -- involutive distribution -- second-order differential equation field -- Lagrangian systems -- inverse problem; Differentiable dynamical systems -- Periodicals; Geometry -- Periodicals; Differentiable dynamical systems; Geometry; Periodicals; 515.39
• DOI: 10.1080/1726037X.2019.1668146
• Languages: English
• ISSNs: 1726-037X

Abstract

Abstract: Suppose that = ( M, M ) is a graded manifold and consider a direct subsheaf of Der M and a graded vector field Γ on ; both satisfying certain conditions. We associate to the graded vector field Γ ∈ Der M, a set of 1-forms and show that if φ ∈ is a non-degenerate graded 1-form and X ∈ Der M such that for some superfunction f on, then the superfunction F = f − J ( φ )( X ) satisfies . This result, generalizes the conditions under which there exist a solution for the inverse problem.