随机流驱动下紧凑子流形体积变化的估计

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2022-05-24 DOI:10.1080/14689367.2022.2078686

Diego S. Ledesma, Robert Andres Galeano Anaya, Fabiano Borges da Silva

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引用次数: 0

摘要

考虑一个紧子流形N，没有黎曼流形M的边界，以及一个与随机微分方程相关的随机流。设为由随机流作用得到的随机紧子流形。在这项工作中，我们提出了随机变量体积的Itô公式，作为主要结果，我们获得了假设Ricci曲率有界的其平均增长的估计。首先分析了子流形为闭合曲线的特殊情况，从而得到了弧长的估计，然后研究了大于或等于2维的紧化子流形的体积变化。此外，我们还将所得结果应用于随机微分方程的向量场为保角消角的特殊情况。

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Estimates for the volume variation of compact submanifolds driven by a stochastic flow

Consider a compact submanifold N without the boundary of a Riemannian manifold M, and a stochastic flow associated with a stochastic differential equation. Let be the random compact submanifold obtained by the action of the stochastic flow. In this work, we present an Itô formula for the volume of the random variable and, as a main result, we obtain estimates for its average growth assuming that Ricci curvature is bounded. We first analyse the particular case where the submanifolds are closed curves, thus obtaining estimates for the arc length, and then we study the volume variation of compact submanifolds of dimensions greater than or equal to 2. In addition, we apply our results to the special case where the vector fields of stochastic differential equation are conformal Killing.

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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences