研究不变函数的轨道空间方法中的工具：地层的合理参数化
Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata
摘要：
在作用于欧几里得空间$\real^n$中的紧致线性群$G$的变换下等变或不变的函数，可以作为定义在群的轨道空间中的函数进行有益的研究。轨道空间是由具有相同轨道类型的$G$ -轨道构成的半代数流形的有限层集合的并集。在本文中，我们提供了一个简单的配方，以获得合理的参数化的地层。我们的结果可以很容易地利用，在许多物理环境中的研究等变或不变的功能是很重要的，例如在确定的模式的自发对称性破缺，在分析相空间和结构相变（朗道理论），在等变分岔理论，在晶体场论和在大多数领域中使用的对称性适应的功能。给出了一个物理上重要的例子，利用的配方，有关的自发极化手性双轴液晶，相对于以前的启发式方法的优势。
英文摘要：
Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the $G$-orbits with the same orbit-type. In this paper we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
