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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)

Abstract

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.

Keywords

Real Axis Real Line Bifurcation Point Transpose Conjugate Relative Minimum 
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References

  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

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