The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L.
Devaney has made these advanced research developments accessible to undergraduate …

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 …

For the family of complex rational functions of the form $ R_ {n, c, a}(z)= z^ n+\dfrac {a}{z^
n}+ c $, known as``Generalized McMullen maps'', for $ a\neq 0$ and $ n\geq 3$ fixed, we …

In this paper, we consider the family of rational maps given by where n≥ 2, and λ is a
complex parameter. When λ= 0 the Julia set is the unit circle, as is well known. But as soon …

In this paper, we study rational functions of the form R n, a, c (z)= zn+ azn+ c, with n fixed
and at least 3, and hold either a or c fixed while the other varies. We locate some …

In this paper, we give a survey of some recent results involving “Mandelpinski necklaces”
that occur in the family of complex rational maps of the form z^ n+ λ/z^ d zn+ λ/zd where λ ∈ …

In this paper we consider singular perturbations of the quadratic polynomial F (z)= z2+ c
where c is the center of a hyperbolic component of the Mandelbrot set, ie, rational maps of …

In this paper, we first work out formulas for nontrivial rational maps of minimal degree that
are invariant under precompositions by the elements of finite Kleinian groups. In fact, up to …

Hausdorff dimension of the boundary of the immediate basin of infinity of McMullen maps |
Proceedings - Mathematical Sciences Skip to main content SpringerLink Account Menu Find a …

Our goal in this paper is to describe the dynamical behavior of singular perturbations of
complex dynamical systems. Singular perturbations occur when a pole is introduced into the …