Topological Dynamics of an Ordinary Differential Equation

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...

Full description

Saved in:
Bibliographic Details
Main Author: Artstein,Zvi
Format: Report
Language:English
Subjects:
DIFFERENTIAL EQUATIONS
MAPPING(TRANSFORMATIONS)
Ordinary differential equations
THEOREMS
Theoretical Mathematics
TOPOLOGY
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.