Related papers: Odometer Based Systems
The main result of this paper is that two large collections of ergodic measure preserving systems, the Odometer Based and the Circular Systems have the same global structure with respect to joinings. The classes are canonically isomorphic…
Given a rank one measure-preserving system defined by cutting and stacking with spacers, we produce a rank one binary sequence such that its orbit closure under the shift transformation, with its unique {nonatomic} invariant probability, is…
We provide a complete characterisation of automaticity of uniformly recurrent substitutive sequences in terms of the incidence matrix of the return substitution of the underlying purely substitutive sequence. This resolves a recent question…
We define an odometer in the Baire space. That is the non-compact space of one sided sequences of natural numbers. We go on to prove that it is topologically conjugated to the dyadic odometer restricted to an appropriate non-compact subset…
A structural analysis of construction schemes is developed. That analysis is used to give simple and new constructions of combinatorial objects which have been of interest to set theorists and topologists. We then continue the study of…
We construct a plethora of Anosov-Katok diffeomorphisms with non-ergodic generic measures and various other mixing and topological properties. We also construct an explicit collection of the set containing the generic points of the system…
The Anosov-Katok method is one of the most powerful tools of constructing smooth volume-preserving diffeomorphisms of entropy zero with prescribed ergodic or topological properties. To measure the complexity of systems with entropy zero,…
In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…
We prove that every infinite minimal subshift with word complexity $p(q)$ satisfying $\limsup p(q)/q < 3/2$ is measure-theoretically isomorphic to its maximal equicontinuous factor; in particular, it has measurably discrete spectrum. Among…
In this paper we give explicit characterizations, based on the cutting and spacer parameters, of (a) which rank-one transformations factor onto a given finite cyclic permutation, (b) which rank-one transformations factor onto a given…
We characterize inverse limits of nilsystems in topological dynamics, via a structure theorem for topological dynamical systems that is an analog of the structure theorem for measure preserving systems. We provide two applications of the…
The mechanisms of comprehension during language processing remains an open question. Classically, building the meaning of a linguistic utterance is said to be incremental, step-by-step, based on a compositional process. However, many…
For dynamical systems with the shadowing property, we provide a method of approximation of invariant measures by ergodic measures supported on odometers and their almost 1-1 extensions. For a topologically transitive system with the…
Due to a result by Glasner and Downarowicz, it is known that a minimal system is mean equicontinuous if and only if it is an isomorphic extension of its maximal equicontinuous factor. The majority of known examples of this type are almost…
Floyd gave an example of a minimal dynamical system which was an extension of an odometer and the fibres of the associated factor map were either singletons or intervals. Gjerde and Johansen showed that the odometer could be replaced by any…
We introduce a toy model of ecosystem assembly for which we are able to map out all assembly pathways generated by external invasions. The model allows to display the whole phase space in the form of an assembly graph whose nodes are…
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…
In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measures and is an almost finite to one extension of its maximal…
For an arbitrary countable discrete infinite group $G$, nonsingular rank-one actions are introduced. It is shown that the class of nonsingular rank-one actions coincides with the class of nonsingular $(C,F)$-actions. Given a decreasing…
This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…