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arXiv · 0704.0949

Conservation laws for invariant functionals containing compositions

Gastao S. F. Frederico·Delfim F. M. Torres
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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.

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Gastao S. F. Frederico, Delfim F. M. Torres. 2007-04-06. Conservation laws for invariant functionals containing compositions. https://doi.org/10.1080/00036810701584583

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