On the dynamics of the McMullen family 𝑅(𝑧)=𝑧^{𝑚}+𝜆/𝑧^{ℓ}

Abstract

In this note we discuss the parameter plane and the dynamics of the rational family R ( z ) = z m + λ / z ℓ R(z)=z^m+\lambda /z^{\ell } , with m ≥ 2 m\ge 2 , ℓ ≥ 1 \ell \ge 1 , and 0 > | λ | > ∞ 0>|\lambda |>\infty .