The dynamical systems approach to differential equations

The Dynamical Systems Approach to Differential Equations

This harmony that human intelligence believes it discovers in nature —does it exist apart from that intelligence? No, without doubt, a reality completely independent of the spirit which conceives it, sees it or feels it, is an impossibility. A world so exterior as that, even if it existed, would be forever inaccessible to us. But what we call objective reality is, in the last analysis, that whi...

Dynamical Systems and Differential Equations

In this manuscript we introduce some important concepts concerning dynamical systems theory. We devote special attention to studying differential equations from a dynamical systems viewpoint. The introduced concepts are illustrated by examples.

Ordinary Differential Equations and Dynamical Systems

Dissipative Partial Differential Equations and Dynamical Systems

This article surveys some recent applications of ideas from dynamical systems theory to understand the qualitative behavior of solutions of dissipative partial differential equations with a particular emphasis on the two-dimensional Navier-Stokes equations.

Ordinary Differential Equations and Dynamical Systems

This manuscript provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore we consider linear equations, the Floquet theorem, and the autonomous...