Abstract
In Chapter 2 we saw that any nonlinear system
with f ∈C1(E) and E an open subset of Rn, has a unique solution Φ t (x0), passing through a point x0 ∈ E at time t=0 which is defined for all t ∈ I(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 | t ∈ I(x)}.
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© 1996 Springer-Verlag New York, Inc.
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Perko, L. (1996). Nonlinear Systems: Global Theory. In: Differential Equations and Dynamical Systems. Texts in Applied Mathematics, vol 7. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0249-0_3
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DOI: https://doi.org/10.1007/978-1-4684-0249-0_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0251-3
Online ISBN: 978-1-4684-0249-0
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