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1.
Nelson G. Markley 《Israel Journal of Mathematics》1975,22(3-4):332-353
Substitution-like minimal sets are a class of symbolic minimal sets on two symbols which includes the discrete substitution minimal sets on two symbols. They are almost automorphic extensions of then-adic integers and they are constructed by using special subsets of then-adics from which the almost automorphic points are determined by following orbits in then-adics. Through their study a complete classification is obtained for substitution minimal sets of constant length on two symbols. Moreover, the classification scheme is such that for specific substitutions the existence or non-existence of an isomorphism can be determined in a finite number of steps. 相似文献
2.
Transversal homoclinic orbits of maps are known to generate a Cantor set on which a power of the map conjugates to the Bernoulli
shift on two symbols. This conjugacy may be regarded as a coding map, which for example assigns to a homoclinic symbol sequence
a point in the Cantor set that lies on a homoclinic orbit of the map with a prescribed number of humps. In this paper we develop
a numerical method for evaluating the conjugacy at periodic and homoclinic symbol sequences in a systematic way. The approach
combines our previous method for computing the primary homoclinic orbit with the constructive proof of Smale's theorem given
by Palmer. It is shown that the resulting nonlinear systems are well conditioned uniformly with respect to the characteristic
length of the symbol sequence and that Newton's method converges uniformly too when started at a proper pseudo orbit. For
the homoclinic symbol sequences an error analysis is given. The method works in arbitrary dimensions and it is illustrated
by examples.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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《Indagationes Mathematicae》2021,32(3):729-735
Recently F. M. Dekking conjectured the form of the subword complexity function for the Fibonacci–Thue–Morse sequence. In this note we prove his conjecture by purely computational means, using the free software Walnut. 相似文献
5.
We study the moments of even order of the generating function of the Thue–Morse sequence and present several conjectures related to these moments.
相似文献
$$\prod\limits_{0 \leqslant r \leqslant n} {(1 - e({2^r}x))} $$
6.
Rafik Belhadef Henri-Alex Esbelin Tahar Zerzaihi 《Mediterranean Journal of Mathematics》2016,13(4):1429-1434
It has been proved that real numbers defined as a limit of continued fractions with a Thue–Morse sequence as the sequence of positive integer partial quotients are transcendental. The same holds for more general sequences of partial quotients. Moreover, transcendence results have been proved for p-adic numbers defined by Hensel development. Here, we tackle the transcendence question in case of p-adic numbers defined as a limit of continued fractions by proving a similar result as the first one. 相似文献
7.
《Indagationes Mathematicae》2021,32(4):847-860
Here, we study some measures that can be represented by infinite Riesz products of 1-periodic functions and are related to the doubling map. We show that these measures are purely singular continuous with respect to Lebesgue measure and that their distribution functions satisfy super-polynomial asymptotics near the origin, thus providing a family of extremal examples of singular measures, including the Thue–Morse measure. 相似文献
8.
We find necessary and sufficient conditions for a symbolic dynamical system to be topologically conjugate to any given constant length substitution minimal system, thus extending the results in Coven et al. (2008) for the Morse and Toeplitz substitutions. 相似文献
9.
Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy. 相似文献
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Xuhua He 《Advances in Mathematics》2007,215(2):469-503
We study the minimal length elements in some double cosets of Coxeter groups and use them to study Lusztig's G-stable pieces and the generalization of G-stable pieces introduced by Lu and Yakimov. We also use them to study the minimal length elements in a conjugacy class of a finite Coxeter group and prove a conjecture in [M. Geck, S. Kim, G. Pfeiffer, Minimal length elements in twisted conjugacy classes of finite Coxeter groups, J. Algebra 229 (2) (2000) 570-600]. 相似文献
13.
We prove that every topological conjugacy between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugacy which extends homeomorphically to the exceptional divisors of their minimal desingularisations. As an application we give an explicit presentation of a finite index subgroup of the mapping class group of the germ of such a singularity. 相似文献
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This paper computes the irreducible characters of the alternating Hecke algebras, which are deformations of the group algebras of the alternating groups. More precisely, we compute the values of the irreducible characters of the semisimple alternating Hecke algebras on a set of elements indexed by minimal length conjugacy class representatives and we show that these character values determine the irreducible characters completely. As an application, we determine a splitting field for the alternating Hecke algebras in the semisimple case. 相似文献
16.
Summary We study closures of conjugacy classes in the Lie algebras of the orthogonal and symplectic groups and determine which ones
are normal varieties. Furthermore we give a complete classification of the minimal singularities which arise in this context,
i.e. the singularities which occur in the open classes in the boundary of a given conjugacy class. In contrast to the results
for the general linear group ([KP1], [KP2]) there are classes with non normal closure; they are branched in a class of codimension
two and give rise to normal minimal singularities. The methods used are (classical) invariant theory and algebraic geometry.
Supported in part by the SFB Theoretische Mathematik, University of Bonn, and by the University of Hamburg 相似文献
17.
P. Christopher Staecker 《Journal of Pure and Applied Algebra》2011,215(7):1702-1710
We give two results for computing doubly-twisted conjugacy relations in free groups with respect to homomorphisms φ and ψ such that certain remnant words from φ are longer than the images of generators under ψ.Our first result is a remnant inequality condition which implies that two words u and v are not doubly-twisted conjugate. Further we show that if ψ is given and φ, u, and v are chosen at random, then the asymptotic probability that u and v are not doubly-twisted conjugate is 1. In the particular case of singly-twisted conjugacy, this means that if φ, u, and v are chosen at random, then u and v are not in the same singly-twisted conjugacy class with asymptotic probability 1.Our second result generalizes Kim’s “bounded solution length”. We give an algorithm for deciding doubly-twisted conjugacy relations in the case where φ and ψ satisfy a similar remnant inequality. In the particular case of singly-twisted conjugacy, our algorithm suffices to decide any twisted conjugacy relation if φ has remnant words of length at least 2.As a consequence of our generic properties we give an elementary proof of a recent result of Martino, Turner, and Ventura, that computes the densities of the sets of injective and surjective homomorphisms from one free group to another. We further compute the expected value of the density of the image of a homomorphism. 相似文献
18.
A. G. Meshkov 《Journal of Mathematical Sciences》2008,151(4):3167-3181
A symmetry classification is presented for integrable two-field third-order evolutionary systems of divergent type. The list
contains thirteen exactly integrable systems. For eleven of them, differential substitutions that relate the systems with
the known systems by Drinfeld-Sokolov, Ito, and Hirota-Satsuma are found. The two remaining systems seem to be new.
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Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 12, No. 7, pp. 141–161,
2006. 相似文献
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20.
M. Keane 《Probability Theory and Related Fields》1968,10(4):335-353
Summary A method for construction of almost periodic points in the shift space on two symbols is developed, and a necessary and sufficient condition is given for the orbit closure of such a point to be strictly ergodic. Points satisfying this condition are called generalized Morse sequences. The spectral properties of the shift operator in strictly ergodic systems arising from generalized Morse sequences are investigated. It is shown that under certain broad regularity conditions both the continuous and discrete parts of the spectrum are non-trivial. The eigenfunctions and eigenvalues are calculated. Using the results, given any subgroup of the group of roots of unity, a generalized Morse sequence can be constructed whose continuous spectrum is non-trivial and whose eigenvalue group is precisely the given group. New examples are given for almost periodic points whose orbit closure is not strictly ergodic. 相似文献