Singular perturbations of complex polynomials

@article{Devaney2013SingularPO,
  title={Singular perturbations of complex polynomials},
  author={Robert L. Devaney},
  journal={Bulletin of the American Mathematical Society},
  year={2013},
  volume={50},
  pages={391-429}
}
  • R. Devaney
  • Published 2 April 2013
  • Mathematics
  • Bulletin of the American Mathematical Society
. In this paper we describe the dynamics of singularly perturbed complex polynomials. That is, we start with a complex polynomial whose dynamics are well understood. Then we perturb this map by adding a pole, i.e., by adding in a term of the form λ/ ( z − a ) d where the parameter λ is complex. This changes the polynomial into a rational map of higher degree and, as we shall see, the dynamical behavior explodes. One aim of this paper is to give a survey of the many different topological… 
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