Conservation laws for invariant functionals containing compositions
Abstract
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.
Cite
@article{arxiv.0704.0949,
title = {Conservation laws for invariant functionals containing compositions},
author = {Gastao S. F. Frederico and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:0704.0949},
year = {2007}
}
Comments
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, 2007