Abstract
Comparable to the importance of the Implicit Function Theorem for the local analysis is the degree of a mapping for any global analysis. Although the theory was originally invented and defined in topology we present an analytical theory developed later. For finite-dimensional continuous mappings it is the Brouwer degree; its extension to infinite dimensions is the Leray–Schauder degree.
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© 2012 Springer Science+Business Media, LLC
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Kielhöfer, H. (2012). Global Theory. In: Bifurcation Theory. Applied Mathematical Sciences, vol 156. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0502-3_3
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DOI: https://doi.org/10.1007/978-1-4614-0502-3_3
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0501-6
Online ISBN: 978-1-4614-0502-3
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