# American Institute of Mathematical Sciences

November  2019, 12(7): 1955-1975. doi: 10.3934/dcdss.2019127

## Branching and bifurcation

 1 Department of Mathematics, University of Maryland, 4176 Campus Dr, College Park, MD 20742, USA 2 INDAM, Dipartimento di Scienze Matematiche, Politecnico di Torino, Duca degli Abruzzi 24, 10129 Torino, Italy

* Corresponding author

Dedicated to Norman Dancer

Received  January 2018 Revised  August 2018 Published  December 2018

Fund Project: J. Pejsachowicz is supported by GNAMPA-INDAM

By relating the set of branch points $\mathcal{B} (f)$ of a Fredholm mapping $f$ to linearized bifurcation, we show, among other things, that under mild local assumptions at a single point, the set $\mathcal B(f)$ is sufficiently large to separate the domain of the mapping. In the variational case, we will also provide estimates from below for the number of connected components of the complement of $\mathcal B(f).$

Citation: Patrick M. Fitzpatrick, Jacobo Pejsachowicz. Branching and bifurcation. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 1955-1975. doi: 10.3934/dcdss.2019127
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