论文标题
无限二维杜邦 - 弗罗贝尼乌斯歧管和斯托克斯现象
Infinite-dimensional Dubrovin-Frobenius manifolds and the Stokes phenomenon
论文作者
论文摘要
我们研究了无限二维2d toda dubrovin-frobenius歧管的杜布罗温方程。我们首先重新审视规范坐标的定义，证明它们自然而然地作为Euler Vector Field乘法运算符的概括性值。然后，我们表明，在不规则的奇异点处具有指数类型行为的杜布罗温方程的形式解决方案不是由其领先顺序确定的，而是取决于无限数量的参数，这与有限维情况中发生的情况相反。接下来，我们获得了沿超电势组合的单位圆圈给出的Dubrovin方程的大型解决方案。观察到这样的家族并不完整并且具有微不足道的单曲，我们研究了通过重新调整一些杰出的正式解决方案获得的较大的弱解决方案家族。这些重新召集的溶液自然出现在与单一相关的对中，最终使我们能够计算Stokes矩阵的无限维度类似物。
We study the Dubrovin equation of the infinite-dimensional 2D Toda Dubrovin-Frobenius manifold at its irregular singularity. We first revisit the definition of the canonical coordinates, proving that they emerge naturally as generalized eigenvalues of the operator of multiplication by the Euler vector field. We then show that the formal solutions to the Dubrovin equation with exponential type behaviour at the irregular singular point are not uniquely determined by their leading order, but instead depend on an infinite number of parameters, contrary to what happens in the finite-dimensional case. Next, we obtain a large family of solutions to the Dubrovin equation given by integrals along the unit circle of certain combinations of the superpotentials. Observing that such a family is not complete and has trivial monodromy, we study a larger family of weak solutions obtained via Borel resummation of some distinguished formal solutions. These resummed solutions naturally appear in monodromy-related pairs, finally allowing us to compute the infinite-dimensional analogue of the Stokes matrices.
