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Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map. The action of this map can be visualized as…
We develop a new framework for branched transport between probability measures which are allowed to vary in time. This framework can be used to model problems where the underlying transportation network displays a branched structure, but…
We conducted a search for very short-period transiting objects in the publicly available Kepler dataset. Our preliminary survey has revealed four planetary candidates, all with orbital periods less than twelve hours. We have analyzed the…
Using the setting of $G$-metric spaces, common fixed point theorems for four maps satisfying the weakly commuting conditions are obtained for various generalized contractive conditions. Several examples are also presented to show the…
We introduce a new coupled map lattice model in which the weak interaction takes place via rare "collisions". By "collision" we mean a strong (possibly discontinuous) change in the system. For such models we prove uniqueness of the SRB…
We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the…
The logistic map is a paradigmatic dynamical system originally conceived to model the discrete-time demographic growth of a population, which shockingly, shows that discrete chaos can emerge from trivial low-dimensional non-linear dynamics.…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
In this paper we introduce some new algebraic and geometric perspectives on networked space communications. Our main contribution is a novel definition of a time-varying graph (TVG), defined in terms of a matrix with values in subsets of…
Most detected transiting planets have orbits which would fit within the one of Mercury, exposing them to intense stellar irradiation and interactions that significantly alter their properties. In contrast, colder planets with longer orbital…
Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their…
New global periodic orbit collision/separatrix reconnection scenarios in the standard nontwist map in different regions of parameter space are described in detail, including exact methods for determining reconnection thresholds that are…
Previously published admissibility conditions for an element of $\{0,1\}^{\mathbb{Z}}$ to be the itinerary of a point of the inverse limit of a tent map are expressed in terms of forward orbits. We give necessary and sufficient conditions…
We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest non-trivial example, namely two…
The two dominant features in the distribution of orbital parameters for close-in exoplanets are the prevalence of circular orbits for very short periods, and the observation that planets on closer orbits tend to be heavier. The first…
In the study of long-time correlations extremely long orbits must be calculated. This may be accomplished much more reliably using fixed-point arithmetic. Use of this arithmetic on the Cray-1 computer is illustrated.
The Super Wide Angle Search for Planets (SuperWASP) is a whole-sky high-cadence optical survey which has searched for exoplanetary transit signatures since 2004. Its archive contains long-term light curves for ~30 million 8-15 V magnitude…