Related Experiment Video
Updated: May 24, 2025
New Variations for Strategy Set-shifting in the Rat
Published on: January 23, 2017
Almost automorphic and bijective factors of substitution shifts
Alvaro Bustos-Gajardo1,2, Johannes Kellendonk3, Reem Yassawi4
1School of Mathematics and Statistics, The Open University, Walton Hall, Kents Hill, Milton Keynes, MK7 6AA UK.
Abstract:
In this article we completely characterise constant length substitution shifts which have a proper almost automorphic factor, or which have a bijective substitution factor such that the factor map is injective on at least one point. Our approach is algebraic: we characterise these dynamical properties in terms of a finite semigroup defined by the substitution. We characterise the existence of almost automorphic factors in terms of Green's -relation and the existence of bijective factors in terms of Green's -relation. Our results are constructive.
Related Concept Videos
01:16Thermal Sigmatropic Reactions: Overview
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in...
02:34Nucleophilic Substitution Reactions
In 1896, the German chemist Paul Walden discovered that he could interconvert pure enantiomeric (+) and (-) malic acids through a series of reactions. This conversion suggested the involvement of optical inversion during the substitution reaction. Further, in 1930, Sir Christopher Ingold described for the first time two different forms of nucleophilic substitution reactions, which are known as SN1 (nucleophilic substitution unimolecular) and SN2 (nucleophilic substitution...
01:34Woodward–Hoffmann Selection Rules and Microscopic Reversibility
01:16Electrophilic Aromatic Substitution: Overview
01:21Factors Affecting Dissolution: Polymorphism, Amorphism and Pseudopolymorphism
Some polymorphic crystals possess lower aqueous solubility than their amorphous counterparts, leading to incomplete absorption. For instance, the oral suspension of Chloramphenicol, which...
01:19Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...