A global bifurcation theorem for critical values in Banach spaces

  • Pablo Amster
  • Pierluigi Benevieri
  • Julián HaddadEmail author


We present a global bifurcation result for critical values of \(C^1\) maps in Banach spaces. The approach is topological based on homotopy equivalence of pairs of topological spaces. For \(C^2\) maps, we prove a particular global bifurcation result, based on the notion of spectral flow.


Global bifurcation Critical values Spectral flow 

Mathematics Subject Classification

58E05 58E07 58J30 



The authors are indebted to the referee for pointing out several valuable comments on a previous version of this work.


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© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemática, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos Aires and IMAS-CONICETBuenos AiresArgentina
  2. 2.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  3. 3.Departamento de Matemática, ICExUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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