含复合的不变泛函的守恒律
Conservation laws for invariant functionals containing compositions
摘要：
复合变分问题的研究是一个相当新的课题，起源于由混沌映射控制的动力系统。现有的结果减少到一个广义欧拉-拉格朗日方程，其中包含一个新的长期涉及逆像的最小化轨迹。在这项工作中，我们证明了一个推广的必要最优性条件的DuBois-Reymond的变分问题的组合。利用新得到的条件证明了一个Noether型定理。我们的主要结果的应用给出了一个问题出现在混乱的设置时，一个考虑的地图是遍历的。
英文摘要：
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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