Related papers: Eventually dendric subshifts
This paper is a survey of the authors' recent results on "abc-surfaces" and the monodromy of their natural Lefschetz fibrations and projections to P^1 x P^1, see (arXiv:0910.2142). The results being surveyed explore various fundamental…
In this paper we study the shifts, which are the shift-invariant and topologically closed sets of configurations over a finite alphabet in $\mathbb{Z}^d$. The minimal shifts are those shifts in which all configurations contain exactly the…
We argue that there are two distinct classes of type I compactification to four dimensions on any space. These two classes are distinguished in a mysterious way by the presence (or absence) of a discrete 6-form potential. In simple…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…
Pinning and depinning of drops on an inclined heterogeneous substrate is studied as a function of the inclination and heterogeneity amplitude. Two types of heterogeneity are considered: a hydrophobic defect that blocks the droplet in front,…
The border-collision normal form describes the local dynamics in continuous systems with switches when a fixed point intersects a switching surface. For one-dimensional cases where the bifurcation creates or destroys only fixed points and…
Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems is difficult and only a few…
We generalize the classical definition of effectively closed subshift to finitely generated groups. We study classical stability properties of this class and then extend this notion by allowing the usage of an oracle to the word problem of…
We prove, for a class of contact manifolds, that the universal cover of the group of contact diffeomorphisms carries a natural partial order. It leads to a new viewpoint on geometry and dynamics of contactomorphisms. It gives rise to…
We study infinite words fixed by a morphism and their derived words. A derived word is a coding of return words to a factor. We exhibit two examples of sets of morphisms which are closed under derivation --- any derived word with respect to…
We show that a large class of non-degenerate second-order (maximally) superintegrable systems gives rise to Hessian structures, which admit natural (Hessian) coordinates adapted to the superintegrable system. In particular, abundant…
In this note we propose an alternative definition for sliding block codes between shift spaces. This definition coincides with the usual definition in the case that the shift space is defined on a finite alphabet, but it encompass a larger…
We establish upper and lower bounds on the maximal number of steps needed to transform a cyclic permutation to the canonical cyclic permutation using conjugation by adjacent transpositions, and on the diameter of the underlying Schreier…
The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de…
We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form…
We provide a systematic treatment of the tenfold way of classifying fermionic systems that naturally allows for the study of those with arbitrary $N$-body interactions. We identify four types of symmetries that such systems can possess,…