## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS

In this work we define a stochastic adding machine associated to a
quadratic base $(F_n)_{n \geq 0}$ formed by recurrent sequences of
order 2. We obtain a Markov chain with states in $\mathbb{Z}^+$ and we
prove that the spectrum of the transition operator associated to
this Markov chain is connected to the
filled Julia sets for a class of endomorphisms in
$\mathbb{C}^2$ of which we study topological properties.

DCDS

We consider in this paper a sequence of complex analytic functions constructed by the following procedure
$f_n(z)=f_{n-1}(z)f_{n-2}(z)+c$, where $c\in\mathbb{C}$ is a parameter. Our aim is to give a thorough dynamical study of this family,
in particular we are able to extend the familiar notions of Julia sets and Green function and to analyze their properties.
As a consequence, we extend some well-known results. Finally we study in detail the case where $c$ is small.

keywords:
holomorphic motion
,
endomorphisms of $\mathbb{C}^2$.
,
Julia sets
,
quasi-circle
,
complex dynamics

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]