Related papers: Random functions from coupled dynamical systems
We determine, up to the equivalence of first-order interdefinability, all structures which are first-order definable in the random partial order. It turns out that these structures fall into precisely five equivalence classes. We achieve…
In Spivak's work, dynamical systems are described in terms of their inputs and outputs in a pictorial way using an operad of wiring diagrams. Each dynamical system is a box with certain inputs and outputs, and multiple dynamical systems are…
Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb{R}^{d})$ called a potential we define its rotation set $R(F)$ as the set of integrals of $F$ with respect to all $T$-invariant…
A function from sequences to their subsequences is called selection function. A selection function is called admissible (with respect to normal numbers) if for all normal numbers, their subsequences obtained by the selection function are…
We consider random sub-graphs of a fixed graph $G=(V,E)$ with large minimum degree. We fix a positive integer $k$ and let $G_k$ be the random sub-graph where each $v\in V$ independently chooses $k$ random neighbors, making $kn$ edges in…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Conformal mapping may be the best-known topic in complex analysis. Any simply connected nonempty domain $\Omega$ in the complex plane ${{\mathbb{C}}}$ (assuming $\Omega\ne {{\mathbb{C}}}$) can be mapped bijectively to the unit disk by an…
We study random dynamical systems on the real line, considering each dynamical system together with the one generated by the inverse maps. We show that there is a duality between forward and inverse behaviour for such systems, splitting…
Active SLAM is the task of actively planning robot paths while simultaneously building a map and localizing within. Existing work has focused on planning paths with occupancy grid maps, which do not scale well and suffer from long term…
The theory of random sets is demonstrated to prove useful for the theory of random operators. A random operator is here defined by requiring the graph to be a random set. It is proved that the spectrum and the set of eigenvalues of random…
A method for determining the orbital parameters of interacting pairs of galaxies is presented and evaluated using artificial data. The method consists of a genetic algorithm which can search efficiently through the very large space of…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
A neural network works as an associative memory device if it has large storage capacity and the quality of the retrieval is good enough. The learning and attractor abilities of the network both can be measured by the mutual information…
As periodic orbit theory works badly on computing the observable averages of dynamical systems with intermittency, we propose a scheme to cooperate with cycle expansion and perturbation theory so that we can deal with intermittent systems…
The chaotic phenomenon of intermittency is modeled by a simple map of the unit interval, the Farey map. The long term dynamical behaviour of a point under iteration of the map is translated into a spin system via symbolic dynamics. Methods…
We consider arbitrary orderings of the edges entering each vertex of the (downward directed) Pascal graph. Each ordering determines an adic (Bratteli-Vershik) system, with a transformation that is defined on most of the space of infinite…
We propose a sequential topology on the space of sub-$\sigma$-algebras of a separable probability space $(\Omega,\mathcal{F},\mathbb{P})$ by linking conditional expectations on $L^{2}$ along sequences of sub-$\sigma$-algebras. The varying…