论文标题
带有旋转三角形的Sierpinski垫片上能量形式的收敛
Convergence of energy forms on Sierpinski gaskets with added rotated triangle
论文作者
论文摘要
我们研究了在空间的收敛序列上的电阻指标和电阻形式的收敛性。作为一种应用，我们研究了带有旋转三角形的Sierpinski垫片上自相似迪里奇的存在和独特性。分形以连续的方式取决于参数。当参数是非理性的时，分形不会在关键的有限后（P.C.F.），并且两个细胞相交的方式无限多种方式。在这种情况下，我们将在P.C.F.上的Dirichlet形式的一些$γ$ -Convergence中定义Dirichlet形式。近似它的分形。
We study the convergence of resistance metrics and resistance forms on a converging sequence of spaces. As an application, we study the existence and uniqueness of self-similar Dirichlet forms on Sierpinski gaskets with added rotated triangles. The fractals depend on a parameter in a continuous way. When the parameter is irrational, the fractal is not post critically finite (p.c.f.), and there are infinitely many ways that two cells intersect. In this case, we will define the Dirichlet form as a limit in some $Γ$-convergence sense of the Dirichlet forms on p.c.f. fractals that approximate it.
