3 research outputs found
Conservation laws for invariant functionals containing compositions
The study of problems of the calculus of variations with compositions is a
quite recent subject with origin in dynamical systems governed by chaotic maps.
Available results are reduced to a generalized Euler-Lagrange equation that
contains a new term involving inverse images of the minimizing trajectories. In
this work we prove a generalization of the necessary optimality condition of
DuBois-Reymond for variational problems with compositions. With the help of the
new obtained condition, a Noether-type theorem is proved. An application of our
main result is given to a problem appearing in the chaotic setting when one
consider maps that are ergodic.Comment: Accepted for an oral presentation at the 7th IFAC Symposium on
Nonlinear Control Systems (NOLCOS 2007), to be held in Pretoria, South
Africa, 22-24 August, 200
Noether's theorem for non-smooth extremals of variational problems with time delay
We obtain a non-smooth extension of Noether's symmetry theorem for variational problems with delayed arguments. The result is proved to be valid in the class of Lipschitz functions, as long as the delayed Euler-Lagrange extremals are restricted to those that satisfy the DuBois-Reymond necessary optimality condition. The important case of delayed variational problems with higher order derivatives is considered as well. © 2013 Taylor & Francis