In the book of the Encyclopaedia of Mathematical Sciences (see below) it says that this is essentially like the time-one map of the unfolding of a vector field with a double zero eigenvalue (Bogdanov-Takens bifurcation), except that the homoclinic loop should be replaced by a transverse intersection.
I do not understand how this part of the homoclinic could apply, as it would create new dynamical structures, in particular a horseshoe.
Someone must have studied this, but I cannot find any references.
The book mentioned above is:
Bifurcation theory and catastrophe theory (enciclopaedia of mathematics - Dynamical Systems V)
Arnold, Afraimovich, Il’yashenko and Shil’nikov
Dear Isabel, local bifurcations, and in particular horseshoe, are explained in Ian Stewart, Martin Golubitsky, The Symmetry Perspective; see also the scientific papers of the two authors on the matter. Gianluca
Thanks Gianluca. I'm aware of that reference, and of work by those authors. However, most of their work concerns differential equations, and here the question is on diffeomorphisms (discrete time), in a context where the two types of dynamics are very different. Also, there is no symmetry in the problem. Thanks for trying!
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