Reachable sets for autonomous systems of differential equations and their topological properties

Sashka Petkova; Andrey Antonov; Rumyana Chukleva

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Reachable sets for autonomous systems of differential equations and their topological properties

机译：微分方程自治系统及其拓扑性质的可到达集合

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摘要

The initial value problems for autonomous systems of differential equations are the main object of this paper. Different variants of the concept reachable sets for the solutions of such systems are introduced. Several conditions for their existence are found and some properties are studied.

机译：微分方程自治系统的初值问题是本文的主要目的。介绍了用于此类系统解决方案的概念可达集的不同变体。找到了它们存在的几个条件并研究了一些特性。

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《American Journal of Applied Mathematics》 |2013年第4期|共6页
作者
Sashka Petkova; Andrey Antonov; Rumyana Chukleva;
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中图分类数学;
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1. Differential Equations for Ellipsoidal Estimates of Reachable Sets for a Class of Control Systems with Nonlinearity and Uncertainty ? [J] . Tatiana F. Filippova IFAC PapersOnLine . 2018,第32期

机译：用于一类具有非线性和不确定性的控制系统的椭圆估计的微分方程
2. On topological properties of solution sets for differential equations in locally convex spaces [J] . Bugajewska D., Bugajewski D. Nonlinear Analysis: An International Multidisciplinary Journal . 2001,第2aPta2期

机译：局部凸空间中微分方程解集的拓扑性质
3. Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems [J] . M. P. Markakis International Journal of Differential Equations . 2010,第1期

机译：一阶二阶非线性自治常微分方程和二维自治系统族的精确解
4. Differential Equations for Ellipsoidal Estimates of Reachable Sets for a Class of Control Systems with Nonlinearity and Uncertainty [C] . Tatiana F. Filippova IFAC Workshop on Control Applications of Optimization . 2019

机译：一类具有非线性和不确定性的控制系统可达套装椭圆估计的微分方程
5. Evolution systems of measures for non-autonomous stochastic differential equations with Lévy noise [D] . Wooster, Robert, III 2009

机译：具有Lévy噪声的非自治随机微分方程测度的演化系统
6. A CLASS OF NONAUTONOMOUS DIFFERENTIAL EQUATIONS REDUCIBLE TO AUTONOMOUS ONES BY AN EXACT METHOD [O] . 1968

机译：一类可精确分解为自治信号的非自治微分方程
7. Level Set Methods for Computing Reachable Sets of Hybrid Systems with Differential Algebraic Equation Dynamics [O] . Mitchell Ian M., Susuki Yoshihiko 2008

机译：具有微分代数方程动力学的混合系统可到达集的水平集方法
8. Two-Dimensional Autonomous Systems of Differential Equations with a First Integral [R] . Wyler, O. 1958

机译：具有第一积分的二维微分方程自治系统

Reachable sets for autonomous systems of differential equations and their topological properties

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