Cicogna G.
Resonant Bifurcations
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ABSTRACT.  We consider dynamical systems depending on one or more real parameters, 
and assuming that, for some ``critical'' value  of the parameters, the 
eigenvalues of the linear part are resonant, we  discuss the 
existence -- under suitable hypotheses -- of a general class of 
bifurcating solutions  in correspondence to this resonance. 
These bifurcating solutions include, as particular cases, the 
usual stationary and  Hopf bifurcations. The main idea 
is to transform the given dynamical system into normal form (in the 
sense of Poincar\'e-Dulac), and  to impose that the normalizing 
transformation is convergent, using the convergence conditions in the 
form given by A. Bruno. Some specially interesting situations, including
the cases of multiple-periodic solutions, and of degenerate eigenvalues 
in the presence of symmetry, are also discussed with some detail.