Related papers: Entropy rate of higher-dimensional cellular automa…
We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique non-trivial homologies. We prove the following two results: if the center foliation is one dimensional,…
Reversible cellular automata are seen as microscopic physical models, and their states of macroscopic equilibrium are described using invariant probability measures. We establish a connection between the invariance of Gibbs measures and the…
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
It has been demonstrated that excitable media with a tree structure performed better than other network topologies, it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift…
We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…
Cellular automata are investigated towards their ability to compute transductions, that is, to transform inputs into outputs. The families of transductions computed are classified with regard to the time allowed to process the input and to…
The concept of independence entropy for symbolic dynamical systems was introduced in [LMP13]. This notion of entropy measures the extent to which one can freely insert symbols in positions without violating the constraints defined by the…
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
A probabilistic cellular automaton (PCA) can be viewed as a Markov chain. The cells are updated synchronously and independently, according to a distribution depending on a finite neighborhood. We investigate the ergodicity of this Markov…
Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…
We perform Transition matrix Monte Carlo simulations to evaluate the entropy of rhombus tilings with fixed polygonal boundaries and 2D-fold rotational symmetry. We estimate the large-size limit of this entropy for D=4 to 10. We confirm…
Commonly studied cellular automata are memoryless and have fixed topology of connections between cells. However by allowing updates of links and short-term memory in cells we may potentially discover novel complex regimes of spatio-temporal…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
We prove that all ($\alpha$-$\beta$)-shifts with $0\le \alpha<1$ and $\beta>2$ are saturated, that is, for any invariant measure, the topological entropy of the set of generic points coincides with the metric entropy.
In the present paper, we introduce a natural extension of AKM-topological entropy for noncompact spaces and prove a variational principle which states that the topological entropy, the supremum of the measure theoretical entropies and the…
We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two…
In this paper, we investigate some ergodic properties of $Z^{2}$-actions $T_{p,n}$ generated by an additive cellular automata and shift acting on the space of all doubly -infinitive sequences taking values in $Z_{m}$.
This paper presents an application of the Infinite Unit Axiom, introduced by Yaroslav Sergeyev, (see [11] - [14]) to the development of one-dimensional cellular automata. This application allows the establishment of a new and more precise…