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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
$$ \dot{x}=f(x) $$
(1)
with fC1(E) and E an open subset of R n , has a unique solution Φ 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 Φ t of the system satisfies (i) Φ0(x)=x and (ii) Φ t +s(x)=Φ t (Φ s (x)) for all x ∈ E and the function Φ(t, x)=Φ t (x) defines a C1-map Φ:Ω → E where Ω={(t, x) ∈R × E | tI(x)}.

Keywords

Periodic Orbit Phase Portrait Stable Limit Cycle Global Theory Quadratic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Lawrence Perko
    • 1
  1. 1.Department of MathematicsNorthern Arizona UniversityFlagstaffUSA

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