Related papers: Periodic points in random substitution subshifts

We consider the structure of aperiodic points in $\mathbb Z^2$-subshifts, and in particular the positions at which they fail to be periodic. We prove that if a $\mathbb Z^2$-subshift contains points whose smallest period is arbitrarily…

Time-varying random objects have been increasingly encountered in modern data analysis. Moreover, in a substantial number of these applications, periodic behaviour of the random objects has been observed. We develop a novel procedure to…

In this paper, we study the periodic and eventually periodic points of affine infra-nilmanifold endomorphisms. On the one hand, we give a sufficient condition for a point of the infra-nilmanifold to be (eventually) periodic. In this way we…

Random substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently…

We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…

In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…

We investigate topological mixing of compatible random substitutions. For primitive random substitutions on two letters whose second eigenvalue is greater than one in modulus, we identify a simple, computable criterion which is equivalent…

This paper proposes a new minimum description length procedure to detect multiple changepoints in time series data when some times are a priori thought more likely to be changepoints. This scenario arises with temperature time series…

Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…

Some properties of random Conley index are obtained and then a sufficient condition for the existence of abstract bifurcation points for both discrete-time and continuous-time random dynamical systems is presented. This stochastic…

Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…

An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…

We give sufficient conditions under which the set of eventually periodic points in the intersection of immediate attracting basins boundaries is non-empty. We give other conditions under which this set is dense in the intersection.

We consider a popular online change-point problem of detecting a transient change in distributions of i.i.d. random variables. For this change-point problem, several change-point procedures are formulated and some advanced results for a…

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…

Change point detection is a crucial aspect of analyzing time series data, as the presence of a change point indicates an abrupt and significant change in the process generating the data. While many algorithms for the problem of change point…

We consider a two-parameter family of random substitutions and show certain combinatorial and topological properties they satisfy. We establish that they admit recognisable words at every level. As a consequence, we get that the subshifts…

We give a sufficient geometric condition for a subshift to be measurably isomorphic to a domain exchange and to a translation on a torus. And for an irreducible unit Pisot substitution, we introduce a new topology on the discrete line and…

We study Hamiltonian diffeomorphisms on symplectic Euclidean spaces that are equal to non-degenerate linear maps at infinity. Under the assumption that there exists an isolated homologically nontrivial fixed point satisfying the twist…

We consider word complexity and topological entropy for random substitution subshifts. In contrast to previous work, we do not assume that the underlying random substitution is compatible. We show that the subshift of a primitive random…