Topological Dynamics of an Ordinary Differential Equation,
Abstract
This is a technical paper that relaxes the conditions under which the mapping Pi(t,(X sub 0),f) = (phi(t,(X sub 0),f),(f sub t)) is a dynamical system, where phi(t,(x sub 0),f) is the solution of dx/dt = f(x,t),x(0) = (x sub 0), and (f sub t) is defined by (f sub t)(x,s) = f(x,t+s). The fact that Pi is a dynamical system has many consequences, including the validity of the LaSalle invariance principle in stability for the nonautonomous system dx/dt = f(x,t). So by casing the conditions the author automatically improves many results.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 31, 1974
- Accession Number
- ADA015760
Entities
People
- Zvi Artstein
Organizations
- Brown University