Uniform stability and chaotic dynamics in nonhomogeneous linear dissipative scalar ordinary differential equations

HIGHER-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS II: Nonhomogeneous Equations

Because the presentation of this material in class will differ from that in the book, I felt that notes that closely follow the class presentation might be appreciated.

Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equations

In this paper, we mainly show the following two statements. (1) A discrete-time Markovian jump linear system is uniformly exponentially stable if and only if it is robustly periodically stable, by using a Gel’fand-Berger-Wang formula proved here. (2) A random linear ODE driven by a semiflow with closing by periodic orbits property is uniformly exponentially stable if and only if it is robustly ...

Linear ordinary differential equations and Schubert calculus

In this short survey we recall some basic results and relations between the qualitative theory of linear ordinary differential equations with real time and the reality problems in Schubert calculus. We formulate a few relevant conjectures.

Fractals in Linear Ordinary Differential Equations

We prove the existence of fractal solutions to a class of linear ordinary differential equations.This reveals the possibility of chaos in the very short time limit of the evolution even of a linear one dimensional dynamical system. PACS Nos.: 02.30.Hq ; 47.53. +n

HIGHER-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS IV: Variable Coefficient Nonhomogeneous Case