A general controllability theorem
On the Darboux transformation. I.
Automorphisms of submanifolds.
On the Darboux transformation. II.
Automorphisms of the family of all Sturm-Liouville equations are investigated. The classical Darboux transformation arises as a particular case of a general result.
On the Mayer problem. II: Examples
On the Mayer problem. I: General principles
Parallelisms between differential and difference equations
The paper deals with the higher-order ordinary differential equations and the analogous higher-order difference equations and compares the corresponding fundamental concepts. Important dissimilarities appear for the moving frame method.
The symmetry reduction of variational integrals
The Routh reduction of cyclic variables in the Lagrange function and the Jacobi-Maupertuis principle of constant energy systems are generalized. The article deals with one-dimensional variational integral subject to differential constraints, the Lagrange variational problem, that admits the Lie group of symmetries. Reduction to the orbit space is investigated in the absolute sense relieved of all accidental structures. In particular, the widest possible coordinate-free approach to the underdetermined...
The symmetry reduction of variational integrals, complement
Some open problems appearing in the primary article on the symmetry reduction are solved. A new and quite simple coordinate-free definition of Poincaré-Cartan forms and the substance of divergence symmetries (quasisymmetries) are clarified. The unbeliavable uniqueness and therefore the global existence of Poincaré-Cartan forms without any uncertain multipliers for the Lagrange variational problems are worth extra mentioning.
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