A harmonic mapping is a univalent harmonic function of one complex variable. We define a family of harmonic mappings on the unit disk whose images are rotationally symmetric “rosettes” with n cusps or n nodes, \(n\ge 3\). These mappings are analogous to the n-cusped hypocycloid, but are modified by Gauss hypergeometric factors, both in the analytic and co-analytic parts. Relative rotations by an angle \(\beta \) of the analytic and anti-analytic parts lead to graphs that have cyclic, and in some cases dihedral symmetry of order n. While the graphs for different \(\beta \) can be dissimilar, the cusps are aligned along axes that are independent of \(\beta \). For certain isolated values of \(\beta \), the boundary function is continuous with arcs of constancy, and has nodes of interior angle \(\pi /2-\pi /n\) instead of cusps.

谐波映射是一个复变量的单价谐波函数。我们在单位磁盘上定义了一组谐波映射，其映像是具有n个尖点或n个节点\（n \ ge 3 \）的旋转对称“ rosettes” 。这些映射类似于n尖的下摆线，但在分析和协分析部分均被高斯超几何因子修改。解析和反解析部分的角度\（\ beta \）的相对旋转会导致图具有循环，在某些情况下具有n阶二面对称。尽管不同\（\ beta \）的图可能不同，但尖点沿独立于\（\ beta \）的轴对齐。对于\（\ beta \）的某些孤立值，边界函数以恒定弧线连续，并且具有内角为\（\ pi / 2- \ pi / n \）的节点而不是尖点。