Numerical Range and Bifurcation Points of a Family of Rational Function

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 47)


Using the Numerical Range Theory we make some interesting observations about the behavior of the dynamics of the family of rational function f λ (x) given by
$$\displaystyle{f_{\uplambda }(x) = 1 - \frac{2\uplambda } {{x}^{2} + \uplambda - 4}}$$
in the neighborhood of the bifurcation point.


Real Axis Real Line Bifurcation Point Transpose Conjugate Relative Minimum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
     Melo, H.,  Cabral, J.: Numerical Range, Numerical Radii and the Dynamics of a Rational Function, Discrete Dynamics and Difference Equations. Proceedings of the twelfth International Conference on Difference Equations and Applications, pp 336–344 (2010)Google Scholar
  2. 2.
     Milnor, J.: Geometry and Dynamics of Quadratic Rational Maps, with an Appendix. In: Milnor, J., Lei, T (eds.) A.K. Peters, Ltd, Wellesley (1993)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Universidade dos AçoresPonta DelgadaPortugal

Personalised recommendations