Related papers: Topological Dynamics of Exponential Maps on their …
This article explores the topology of Pseudo-B\"ottcher totally invariant connected components of the wandering set in dynamical systems generated by on-invertible inner (open surjective isolated) mappings of compact surfaces. We describe…
The exponential map that characterises the flows of vector fields is the key in understanding the basic structural attributes of control systems in geometric control theory. However, this map does not exists due to the lack of completeness…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
We investigate the set $I$ of parameters $\kappa$ for which the singular value of $z\mapsto e^z+\kappa$ converges to $\infty$. The set $I$ consists of uncountably many parameter rays, plus landing points of some of these rays. We show that…
Let $f_\theta(z)=e^{2\pi i\theta}z+z^2$ be the quadratic polynomial having an indifferent fixed point at the origin. For any bounded type irrational number $\theta\in\mathbb{R}\setminus\mathbb{Q}$ and any rational number $\nu\in\mathbb{Q}$,…
Our main result states that, under an exponential map whose Julia set is the whole complex plane, on each piecewise smooth Jordan curve there is a point whose orbit is dense. This has consequences for the boundaries of nice sets, used in…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
It is proved that the Chebyshev's method applied to an entire function $f$ is a rational map if and only if $f(z) = p(z) e^{q(z)}$, for some polynomials $p$ and $q$. These are referred to as rational Chebyshev maps, and their fixed points…
We show that if there exists a topologically expansive homeomorphism on a uniform space, then the space is always a regular space. Through examples we show that in general composition of topologically expansive homeomorphisms need not be…
We consider random iteration of exponential entire functions, i.e. of the form ${\mathbb C}\ni z\mapsto f_\lambda(z):=\lambda e^z\in\mathbb C$, $\lambda\in{\mathbb C}\setminus \{0\}$. Assuming that $\lambda$ is in a bounded closed interval…
We show that for any quasimeromorphic mapping with an essential singularity at infinity, there exist points whose iterates tend to infinity arbitrarily slowly. This extends a result by Nicks for quasiregular mappings, and Rippon and…
One of the most fascinating and puzzling aspects of non-Hermitian systems is their spectral degeneracies, i.e., exceptional points (EPs), at which both eigenvalues and eigenvectors coalesce to form a defective state space. While coupled…
We study the dynamics of iterated cosine maps $E\colon z \mapsto ae^z+be^{-z},$ with $a,b \in \C\setminus \{0\}$. We show that the points which converge to infinity under iteration are organized in the form of rays and, as in the…
Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…
In holomorphic dynamics, complex box mappings arise as first return maps to well-chosen domains. They are a generalization of polynomial-like mapping, where the domain of the return map can have infinitely many components. They turned out…
Let $E_{\la}(z)=\la {\rm exp}(z), \ \lambda\in \mathbb C$ be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $\la$, the set of points in $\mathbb…
We give a combinatorial classification of postsingularly finite exponential maps in terms of external addresses starting with the entry 0. This is an extension of the classification results for critically preperiodic polynomials \cite{BFH}…
This paper discusses the thermodynamic properties for certain time-dependent dynamical systems. In particular, we are interested in time-dependent dynamical systems with the specification property. We show that each time-dependent dynamical…
It is well known that, for chaotic systems, the production of relevant entropy (Boltzmann-Gibbs) is always linear and the system has strong (exponential) sensitivity to initial conditions. In recent years, various numerical results indicate…
We investigate the temporal dynamics of the Ikeda Map with Balanced Gain and Loss and in the presence of feedback loops with saturation nonlinearity. From the bifurcation analysis, we find that the temporal evolution of optical power…