On noninvertible mappings of the plane: Eruptions.

@article{Billings1996OnNM,
  title={On noninvertible mappings of the plane: Eruptions.},
  author={Lora Billings and James H. Curry},
  journal={Chaos},
  year={1996},
  volume={6 2},
  pages={108-120}
}
In this paper we are concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or "eruption," is described. A fundamental role is played by the interactions of fixed points and singular curves. Other critical elements in the phase space include periodic points and an invariant line. The dynamics along the invariant line, in two of the examples, reduces to the one-dimensional Newton's method which is conjugate to a… CONTINUE READING