Related papers: Universality in Multidimensional Symbolic Dynamics
Two cellular automata are strongly conjugate if there exists a shift-commuting conjugacy between them. We prove that the following two sets of pairs $(F,G)$ of one-dimensional one-sided cellular automata over a full shift are recursively…
Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both…
We introduce the entropy rate of multidimensional cellular automata. This number is invariant under shift-commuting isomorphisms; as opposed to the entropy of such CA, it is always finite. The invariance property and the finiteness of the…
According to a conjecture of Lindenstrauss and Tsukamoto, a topological dynamical system $(X,T)$ is embeddable in the $d$-cubical shift $(([0,1]^{d})^{\mathbb{Z}},\ shift)$ if both its mean dimension and periodic dimension are strictly…
There may be structural principles pertaining to the general behavior of systems that lead to similarities in a variety of different contexts. Classic examples include the descriptive power of fractals, the importance of surface area to…
We give strongly aperiodic subshifts of finite type on every hyperbolic surface group; more generally, for each pair of expansive primitive symbolic substitution systems with incommensurate growth rates, we construct strongly aperiodic…
In this paper we study the dimension spectrum of general conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We perform a comprehensive study of the dimension spectrum addressing questions…
Hochman asked whether there exists a cellular automaton $F$ such that every cellular automaton is a factor of $F$ in the dynamical sense. In particular, we do not require the factor map to commute with the spatial shifts. We show that no…
A large class of real $3$-dimensional nilpotent polynomial vector fields of arbitrary degree is considered. The aim of this work is to present general properties of the discrete and continuous dynamical systems induced by these vector…
The addition of a topologically massive term to an admittedly non-unitary three-dimensional massive model, be it an electromagnetic system or a gravitational one, does not cure its non-unitarity. What about the enlargement of avowedly…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
$\lambda$-graph systems are labeled Bratteli diagram with shift operations. They present subshifts. Their matrix presentations are called symbolic matrix systems. We define skew products of $\lambda$-graph systems and study extensions of…
In this paper, some characterizations about transitivity, mildly mixing property, $\mathbf{a}$-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh's extensions restricted on some invariant closed subsets of the space of…
A new universality of Lyapunov spectra {\lambda_i} is shown for Hamiltonian systems. The universality appears in middle energy regime and is different from another universality which can be reproduced by random matrices in the following two…
Let $D \subset {\mathbb R}^d,\: d \geqslant 2,$ be the union of a finite collection of pairwise disjoint strictly convex compact obstacles. Let $\mu_j \in {\mathbb C},\: {\rm Im}\: \mu_j > 0,$ be the resonances of the Laplacian in the…
In [DKY], it was conjectured that there is a uniform bound $B$, depending only on the degree $d$, so that any pair of holomorphic maps $f, g :\mathbb{P}^1\to\mathbb{P}^1$ with degree $d$ will either share all of their preperiodic points or…
We explore universal critical behavior in models with two competing order parameters, and an O(N)+O(M) symmetry for dimensions $d \leq 3$. In d=3, there is always exactly one stable Renormalization Group fixed point, corresponding to…
Universal theories are a broad class of well-motivated microscopic dynamics of the electroweak sector that go beyond the Standard Model description. The long distance physics is described by electroweak parameters which correspond to local…
The effective actions of gauge bosons, fermions and scalars, which are obtained within the hard-loop approximation, are shown to have unique forms for a whole class of gauge theories including QED, scalar QED, super QED, pure Yang-Mills,…
According to the celebrated Jaworski Theorem, a finite dimensional aperiodic dynamical system $(X,T)$ embeds in the $1$-dimensional cubical shift $([0,1]^{\mathbb{Z}},shift)$. If $X$ admits periodic points (still assuming $\dim(X)<\infty$)…