The aim of this article is to apply a Floer theory to study symmetric periodic Reeb orbits. We define positive equivariant wrapped Floer homology using a (anti-)symplectic involution on a Liouville domain and investigate its algebraic properties. By a careful analysis of index iterations, we obtain a non-trivial lower bound on the minimal number of geometrically distinct symmetric periodic Reeb orbits on a certain class of real contact manifolds. This includes non-degenerate real dynamically convex star-shaped hypersurfaces in ${\mathbb {R}}^{2n}$ which are invariant under complex conjugation. As a result, we give a partial answer to the Seifert conjecture on brake orbits in the contact setting.

本文的目的是应用 Floer 理论来研究对称周期性 Reeb 轨道。我们使用刘维尔域上的（反）辛对合来定义正等变包裹的 Floer 同调性，并研究其代数性质。通过对索引迭代的仔细分析，我们在某一类实际接触流形上获得了几何上不同的对称周期性 Reeb 轨道的最小数量的非平凡下界。 这包括${\mathbb {R}}^{2n}$ 中的非退化实动态凸星形超曲面， 它们在复共轭下是不变的。因此，我们对接触设置中的制动轨道上的 Seifert 猜想给出了部分答案。