Abstract
In this section we shall assemble some tools which are useful in the proofs of bifurcation theorems. We begin with some general properties of flows and semiflows (≡ nonlinear groups and nonlinear semigroups) following Chernoff-Marsden [1,2]. These include various important continuity and smoothness properties. Next, we give a basic criterion for when a semiflow consists of smooth mappings following Dorroh-Marsden [1].
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© 1976 Springer-Verlag New York Inc.
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Marsden, J.E., McCracken, M. (1976). Notes on Nonlinear Semigroups. In: The Hopf Bifurcation and Its Applications. Applied Mathematical Sciences, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6374-6_19
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DOI: https://doi.org/10.1007/978-1-4612-6374-6_19
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90200-5
Online ISBN: 978-1-4612-6374-6
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