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Title: Conservation laws for invariant functionals containing compositions
Author: Frederico, G.S.F.
Torres, D.F.M.
Keywords: DuBois-Reymond condition
Functionals containing compositions
Noether's theorem
Optimal control
Variational calculus
Issue Date: 2007
Publisher: IFAC
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. Copyright © 2007 IFAC.
Peer review: yes
ISBN: 978-3-902661-28-9
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Appears in Collections:DMat - Comunicações

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