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The purpose of this study is to indicate fundamental propositions of the pre-image entropy related to a system proposed by Bufetov [Bufetov A. Topological entropy of free semigroup actions and skew-product transformations. J Dyn Control Syst 1999;5:137–143. 1.] for generating free semigroup actions. This study reveals the formula for the pre-image entropy of skew-product transformation with respect to the one-sided shift space. Finally, one example is presented to show how to obtain the pre-image entropy value for the skew-product transformation. 相似文献
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《Topology and its Applications》2009,156(2):251-261
We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of chain transitive maps. These notions of recurrence are defined using ε-chains, and the minimal lengths of these ε-chains give a way to measure recurrence time (chain recurrence and chain mixing times). We give upper and lower bounds for these recurrence times and relate the chain mixing time to topological entropy. 相似文献
4.
David Richeson 《Topology and its Applications》2008,156(2):251-261
We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of chain transitive maps. These notions of recurrence are defined using ε-chains, and the minimal lengths of these ε-chains give a way to measure recurrence time (chain recurrence and chain mixing times). We give upper and lower bounds for these recurrence times and relate the chain mixing time to topological entropy. 相似文献
5.
This paper introduces both notions of topological entropy and invariance entropy for semigroup actions on general topological spaces. We use the concept of admissible family of open coverings to extending and studying the notions of Adler–Konheim–McAndrew topological entropy, Bowen topological entropy, and invariance entropy to the general theory of topological dynamics. 相似文献
6.
We describe the notions of synchronization and simplification with respect to a given subsemigroup P of a semigroup S in terms of the syntactic semigroup of P. These notions derive from coding theory, which corresponds to the case where P is a free subsemigroup of a free semigroup; we apply the results to give a unified account of several theorems previously published. 相似文献
7.
We prove some results concerning the entropy of continuous and almost continuous functions. We first introduce the notions of bundle entropy and (strong) entropy points and then we study properties of these notions in connection with the theory of multifunctions. Based on these facts we give theorems about approximation of functions defined and assuming their values on compact manifold by functions having strong entropy points. 相似文献
8.
Francis T. Christoph Jr. 《Semigroup Forum》1970,1(1):224-231
In [6] Rothman investigated the problem of embedding a topological semigroup in a topological group. He defined a concept
calledProperty F and showed that Property F is a necessary and sufficient condition for embedding a commutative, cancellative topological
semigroup in its group of quotients as an open subset. This paper announces a generalization of Rothman’s result by definingProperty E and stating that a completely regular topological semigroup S can be embedded in a topological group by a topological isomorphism
if and only if S can be embedded (algebraically) in a group and S has Property E. Property E is defined by first constructing
a free topological semigroup (Theorem 1.1). This construction resembles the one in [4] for a free topological group. Full
details, examples, and other embedding results will appear elsewhere.
Some of the results in this paper were contained in the author’s doctoral dissertation written at Rutgers University under
Professor Louis F. McAuley. 相似文献
9.
51.IntroductionandPreliminariesThroughoutthispaper(X,11'if)denotesanormedspaceandN(11'II)denotesthecollectionofallnormsonXwhichareequivalentto11'11.Foreach11'if'6N(II'II)andeachr>0,letX.(ll'II')~{xEX:Ilxll'5r}andX?(ll'if')~{xEX.Ilxll'相似文献
10.
We study the maximal subgroups of free idempotent generated semigroups on a biordered set by topological methods. These subgroups are realized as the fundamental groups of a number of 2-complexes naturally associated to the biorder structure of the set of idempotents. We use this to construct the first example of a free idempotent generated semigroup containing a non-free subgroup. 相似文献
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We give a full topological characterization of omega limit sets of continuous maps on graphs and we show that basic sets have similar properties as in the case of the compact interval. We also prove that the presence of distributional chaos, the existence of basic sets, and positive topological entropy (among other properties) are mutually equivalent for continuous graph maps. 相似文献
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The notion of metrized order (antimetric) on a topological group is characterized by three equivalent systems of axioms and connected with pointed locally generated semigroups. In the present paper, these notions are discussed and new results are announced. The main result is an analog of the following fact in metric geometry: every left-invariant inner metric on a Lie group is Finsler (maybe, nonholonomic). In the situation considered, a norm is replaced by an antinorm, and a metric by an antimetric. Examples are given, showing the complexity of these structures and their prevalence. Among them are: a nonholonomic antimetric on Heisenberg group, an antimetric on a nonnilpotent group admitting dilatations, a pointed locally generated semigroup in the Hilbert space with trivial tangent cone, antinorms connected with the Brunn–Minkowski inequality and Shannon entropy, a discontinuous antinorm on a Lie algebra determining a continuous antimetric on the Lie group, and an example of the converse situation. Problems are formulated. Bibliography: 47 titles. 相似文献
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In this paper,a new type of entropy,directional preimage entropy including topological and measure theoretic versions for■-actions,is introduced.Some of their properties including relationships and the invariance are obtained.Moreover,several systems including■-actions generated by the expanding maps,■-actions defined on finite graphs and some infinite graphs with zero directional preimage branch entropy are studied. 相似文献
15.
Ll. Alsedà D. Juher P. Mumbrú 《Proceedings of the American Mathematical Society》2001,129(10):2941-2946
This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.
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Nguyen Tien Zung 《Bulletin of the Brazilian Mathematical Society》2011,42(4):853-867
We give a notion of entropy for general gemetric structures, which generalizes well-known notions of topological entropy of vector fields and geometric entropy of foliations, and which can also be applied to singular objects, e.g. singular foliations, singular distributions, and Poisson structures. We show some basic properties for this entropy, including the additivity property, analogous to the additivity of Clausius-Boltzmann entropy in physics. In the case of Poisson structures, entropy is a new invariant of dynamical nature, which is related to the transverse structure of the characteristic foliation by symplectic leaves. 相似文献
17.
The combinatorial simple principal ideal semigroups generated by two elements were described by L. Megyesi and G. Pollák.
The ‘most general’ among them is called the Rédei semigroup. The ‘most special’ combinatorial simple principal ideal semigroup
generated by two elements is the bicyclic semigroup. D. B. McAlister determined the compatible semilattice orders on the bicyclic
semigroup. Our aim is to study the compatible semilattice orders on the homomorphic images of the Rédei semigroup. We prove
that there are four compatible total orders on these semigroups. We show that on the Rédei semigroup, the total orders are
the only compatible semilattice orders. Moreover, on each proper homomorphic image of the Rédei semigroup, we give a compatible
semilattice order which is not a total order.
Communicated by Mária B. Szendrei 相似文献
18.
We introduce an algorithm to compute the topological entropy of piecewise monotone maps with at most three different kneading sequences, with prescribed accuracy. As an application, we compute the topological entropy of 3-periodic sequences of logistic maps, disproving a commutativity formula for topological entropy with three maps, and analyzing the dynamics Parrondo’s paradox in this setting. 相似文献
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Steffen Lewitzka 《Logica Universalis》2007,1(2):243-276
What is a logic? Which properties are preserved by maps between logics? What is the right notion for equivalence of logics?
In order to give satisfactory answers we generalize and further develop the topological approach of [4] and present the foundations
of a general theory of abstract logics which is based on the abstract concept of a theory. Each abstract logic determines
a topology on the set of theories. We develop a theory of logic maps and show in what way they induce (continuous, open) functions
on the corresponding topological spaces. We also establish connections to well-known notions such as translations of logics
and the satisfaction axiom of institutions [5]. Logic homomorphisms are maps that behave in some sense like continuous functions
and preserve more topological structure than logic maps in general. We introduce the notion of a logic isomorphism as a (not
necessarily bijective) function on the sets of formulas that induces a homeomorphism between the respective topological spaces
and gives rise to an equivalence relation on abstract logics. Therefore, we propose logic isomorphisms as an adequate and
precise notion for equivalence of logics. Finally, we compare this concept with another recent proposal presented in [2].
This research was supported by the grant CNPq/FAPESB 350092/2006-0. 相似文献
20.
Alica Miller 《Topology and its Applications》2011,158(3):291-297
A theory of semiflows with a discrete acting topological semigroup was developed in the 2000 paper by D. Ellis, R. Ellis and M. Nerurkar (2000) [3]. A theory for the case of an arbitrary acting topological semigroup has still to be developed. This paper can be considered as the beginning of an attempt in that direction.We introduce the notion of the envelope of a g-syndetic subsemigroup of the acting topological semigroup in a semiflow and prove various properties of this notion. We give some examples and deduce some statements from other papers as corollaries of our statements. 相似文献