Abstract
In this section, we consider an autonomous RFDE(f) and first discuss the most elementary properties of the solutions near a constant solution x = 0. More specifically, we prove that if no eigenvalues of the linear variational equation lie on the imaginary axis; that is, x = 0 is hyperbolic, then there is a saddle point at x = 0.
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© 1977 Springer-Verlag New York Inc.
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Hale, J.K. (1977). Behavior near equilibrium and periodic orbits for autonomous equations. In: Theory of Functional Differential Equations. Applied Mathematical Sciences, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9892-2_11
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DOI: https://doi.org/10.1007/978-1-4612-9892-2_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9894-6
Online ISBN: 978-1-4612-9892-2
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