Nonlinear Systems: Global Theory

  • Lawrence Perko
Part of the Texts in Applied Mathematics book series (TAM, volume 7)

Abstract

In Chapter 2 we saw that any nonlinear system
$$ \dot x = f\left( x \right), $$
(1)
with ∈ C 1(E) and E an open subset of R n , has a unique solution ø t (x0), passing through a point x0E at time t = 0 which is defined for all tI(x0), the maximal interval of existence of the solution. Furthermore, the flow ø t of the system satisfies (i) ø0(x)=x and (ii) ø t+s (x)=ø t s (x)) for all x ∈ E; and the function ø(t, x)=ø t (x) defines a C 1-map ø: Ω→ E where Ω, = {(t, x) ∈ R × E|tI(x)}.

Keywords

Manifold Peri Sine Dinates Librium 

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Lawrence Perko
    • 1
  1. 1.FlagstaffUSA

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