. . . . . . . "[2C66066AC44D]" . . "In this paper, a general Hamiltonian theory for Lagrangian systems on fibred manifolds is proposed. The concept of a Lepagean (n+1)-form is defined, generalizing Krupka's concept of a Lepagean n-form. Lepagean (n+1)-forms are used to study Lagrangian andHamiltonian systems. Innovations and new results concern the following: a Lagrangian system is considered as an equivalence class of local Lagrangians; a Hamiltonian system is associated with an Euler-Lagrange form (not with a particular Lagrangian); Hamilton equations are based upon a Lepagean (n+1)-form, and cover Hamilton-De Donder equations as a special case. First-order Hamiltonian systems, namely those carying higher-degree contact components of the corresponding Lepagean forms, are studied in detail. The presented geometric setting leads to a new understanding of the concepts of regularity and Legendre transformation in the calculus of variations, relating them directly to the properties of the arising exterior differential systems." . "2" . "1"^^ . "Hamiltonian field theory"@en . "RIV/47813059:19610/02:00000084!RIV/2003/GA0/196103/N" . "647387" . "In this paper, a general Hamiltonian theory for Lagrangian systems on fibred manifolds is proposed. The concept of a Lepagean (n+1)-form is defined, generalizing Krupka's concept of a Lepagean n-form. Lepagean (n+1)-forms are used to study Lagrangian andHamiltonian systems. Innovations and new results concern the following: a Lagrangian system is considered as an equivalence class of local Lagrangians; a Hamiltonian system is associated with an Euler-Lagrange form (not with a particular Lagrangian); Hamilton equations are based upon a Lepagean (n+1)-form, and cover Hamilton-De Donder equations as a special case. First-order Hamiltonian systems, namely those carying higher-degree contact components of the corresponding Lepagean forms, are studied in detail. The presented geometric setting leads to a new understanding of the concepts of regularity and Legendre transformation in the calculus of variations, relating them directly to the properties of the arising exterior differential systems."@en . "0"^^ . . . "1"^^ . "Journal of Geometry and Physics" . "IT - Italsk\u00E1 republika" . . "0"^^ . . . . "40"^^ . . . . "Hamiltonian field theory"@en . "Krupkov\u00E1, Olga" . "Hamiltonian field theory" . "19610" . "Lagrangian; Poincar\u00E9-Cartan form; Lepagean n-form; Lepagean (n+1)-form; Hamilton extremal;Hamilton equations; Hamilton-De Donder equations; Regularity; Legendre transformation"@en . . "Hamiltonian field theory" . . "43" . . . "RIV/47813059:19610/02:00000084" . . . "P(GA201/00/0724), Z(MSM 192400002)" . "93;132" . "0393-0440" .