Mathematics – Optimization and Control
Scientific paper
2007-04-06
Applicable Analysis, Volume 86, Issue 9, 2007, pp. 1117-1126.
Mathematics
Optimization and Control
Accepted for an oral presentation at the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), to be held in Pretoria
Scientific paper
10.1080/00036810701584583
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.
Frederico Gastao S. F.
Torres Delfim F. M.
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