aequationes mathematicae

, Volume 52, Issue 1, pp 180–194 | Cite as

Iteration of a quaternionic quadratic family

  • Meta Škapin-Rugelj
Research Papers

Summary

Since multiplication of quaternions is not commutative, a quadratic function in quaternions reads
$$q\left( X \right) = \sum\limits_i {F_i } XG_i XH_i + \sum\limits_j {J_j XK_i + C.} $$
Contrary to the complex case, this form cannot be reduced to a one-parameter casegQ(X) = X2 + Q. In the paper the quadratic familiesf = ΛX(1 − X) andhΘ = ΘX2 + 1 are considered. Although they have many common properties, they are not linearly conjugate unless Λ and Θ are real.

AMS (1991) subject classification

Primary 58FXX Secondary 30G35 

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Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Meta Škapin-Rugelj
    • 1
  1. 1.Faculty of Civil Engineering and GeodesyUniversity of LjubljanaLjubljanaSlovenia

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