The Experts below are selected from a list of 58287 Experts worldwide ranked by ideXlab platform
Qiao Zong-min - One of the best experts on this subject based on the ideXlab platform.
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Non-wandering set of Continuous Map on Y-space
Journal of Hefei Teachers College, 2009Co-Authors: Qiao Zong-minAbstract:Here we study the topological structure of non-wandering set of self-Continuous Map on Y-space,we prove that for any x∈Yand x∈W(f)-P(f),then x∈Ω～(f).we extend the corresponding results on interval and circle,and improve the result on tree Map.
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Continuous Map having the weak specification property and chaos
Journal of Anhui University, 2004Co-Authors: Qiao Zong-min, Gu Rong-baoAbstract:For conntinuous Map of compact metric space,we study the relationships between the weak specification property and invariant probability measure. Then we prove that the system with weak specification must have a Continuous Map f:X→X with an invariant probability measure m ,such that Suppm=X and M(f)=X.
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Continuous Map considering the weak specification property and chaos
Journal of Hefei University of Technology, 2004Co-Authors: Qiao Zong-minAbstract:Specification is an important dynamical property, and it is equivalent to topological mixing for Continuous Mapping on the interval and the tree,and for the Continuous Map of compact metric space,POTP and topological mixing imply weak specification. Here studied are the relationships between the weak specification property and all kinds of chaos. It is proved that the system with weak specification must be Li-Yorke chaos, Ruelle-Takens chaos,chaos everywhere,and having the property of P.
V. Tzannes - One of the best experts on this subject based on the ideXlab platform.
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A Moore strongly rigid space
Canadian Mathematical Bulletin, 1991Co-Authors: V. TzannesAbstract:AbstractIt is proved that for every Hausdorff space ℝ and for every Hausdorff (regular or Moore) space X, there exists a Hausdorff (regular or Moore, respectively) space S containing X as a closed subspace and having the following properties: la)Every Continuous Map of S into ℝ is constant.b)For every point x of S and every open neighbourhood U of x there exists an open neighbourhood V of x, V ⊆ U such that every Continuous Map of V into ℝ is constant.2)Every Continuous Map f of S into S (f ≠ identity on S) is constant. In addition it is proved that the Fomin extension of the Moore space S has these properties.
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Two countable Hausdorff almost regular spaces every contiunous Map of which into every Urysohn space is constant
International Journal of Mathematics and Mathematical Sciences, 1991Co-Authors: V. TzannesAbstract:We construct two countable, Hausdorff, almost regular spaces I(S), I(T) having the following properties: (1) Every Continuous Map of I(S) (resp, I(T)) into every Urysohn space is constant (hence, both spaces are connected). (2) For every point of I(S) (resp. of I(T)) and for every open neighbourhood U of this point there exists an open neighbourhood V of it such that V⫅U and every Continuous Map of V into every Urysohn space is constant (hence both spaces are locally connected). (3) The space I(S) is first countable and the space I(T) nowhere first countable. A consequence of the above is the construction of two countable, (connected) Hausdorff, almost regular spaces with a dispersion point and similar properties. Unfortunately, none of these spaces is Urysohn.
Jaroslav Smítal - One of the best experts on this subject based on the ideXlab platform.
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A “universal” dynamical system generated by a Continuous Map of the interval
Proceedings of the American Mathematical Society, 2000Co-Authors: Jaroslav Smítal, D. PokludaAbstract:In this paper we show that there is a Continuous Map f : I → I of the interval such that any ω-limit set W of any Continuous Map g : I → I can be transformed by a homeomorphism I → I to an ω-limit set W of f . Consequently, any nowhere-dense compact set and any finite union of compact intervals is a homeomorphic copy of an ω-limit set of f .
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a universal dynamical system generated by a Continuous Map of the interval
Proceedings of the American Mathematical Society, 2000Co-Authors: Jaroslav Smítal, D. PokludaAbstract:In this paper we show that there is a Continuous Map f : I → I of the interval such that any ω-limit set W of any Continuous Map g : I → I can be transformed by a homeomorphism I → I to an ω-limit set W of f . Consequently, any nowhere-dense compact set and any finite union of compact intervals is a homeomorphic copy of an ω-limit set of f .
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the space of omega limit sets of a Continuous Map of the interval
Transactions of the American Mathematical Society, 1996Co-Authors: Alexander Blokh, A M Bruckner, Paul D Humke, Jaroslav SmítalAbstract:We first give a geometric characterization of ω-limit sets. We then use this characterization to prove that the family of ω-limit sets of a Continuous interval Map is closed with respect to the Hausdorff metric. Finally, we apply this latter result to other dynamical systems.
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A Chaotic Continuous Map Generates All Probability Distributions
Journal of Mathematical Analysis and Applications, 1993Co-Authors: F. Balibrea, Jaroslav SmítalAbstract:Let ƒ be a Continuous Map of the compact unit interval I = [0, 1], such that ƒ2, the second iterate of ƒ, is topologically transitive in I. If for some x and y in I and any t in I there exists lim(1/n) # {i ≤ n; |ƒi(x) − ƒi(y)| < t} for n → ∞, denote it by φxy(t). In the paper we consider the class F(ƒ) if all φxy. The main results are that F(ƒ) is convex and pointwise closed. Using this we show that F(ƒ) is always bigger than the class D(ƒ) of probability distributions generated analogously by single trajectories (and corresponding to the class of probability invariant measures of ƒ), and prove that there are universal generators of probability distributions, i.e., Maps ƒ such that F(ƒ) is the class M of all non-decreasing functions I ⇒ I (contrary to this, D(ƒ) ⊃ M for no ƒ). These results can be extended to more general Continuous Maps. One of the possible applications is to use the size of F(ƒ) as a measure of the degree of chaos of ƒ.
Michel Coornaert - One of the best experts on this subject based on the ideXlab platform.
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Mean Topological Dimension for Continuous Maps
Universitext, 2015Co-Authors: Michel CoornaertAbstract:In this chapter, the term “dynamical system” refers to a pair (X,T), where X is a topological space and T a Continuous Map from X into itself.
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Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property
Illinois Journal of Mathematics, 2015Co-Authors: Michel Coornaert, Tullio Ceccherini-silbersteinAbstract:Let $X$ be a compact metrizable space equipped with a Continuous action of a countable amenable group $G$. Suppose that the dynamical system $(X,G)$ is expansive and is the quotient by a uniformly bounded-to-one factor Map of a strongly irreducible subshift. Let $\tau \colon X \to X$ be a Continuous Map commuting with the action of $G$. We prove that if there is no pair of distinct $G$-homoclinic points in $X$ having the same image under $\tau$ then $\tau$ is surjective.
D. Pokluda - One of the best experts on this subject based on the ideXlab platform.
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A “universal” dynamical system generated by a Continuous Map of the interval
Proceedings of the American Mathematical Society, 2000Co-Authors: Jaroslav Smítal, D. PokludaAbstract:In this paper we show that there is a Continuous Map f : I → I of the interval such that any ω-limit set W of any Continuous Map g : I → I can be transformed by a homeomorphism I → I to an ω-limit set W of f . Consequently, any nowhere-dense compact set and any finite union of compact intervals is a homeomorphic copy of an ω-limit set of f .
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a universal dynamical system generated by a Continuous Map of the interval
Proceedings of the American Mathematical Society, 2000Co-Authors: Jaroslav Smítal, D. PokludaAbstract:In this paper we show that there is a Continuous Map f : I → I of the interval such that any ω-limit set W of any Continuous Map g : I → I can be transformed by a homeomorphism I → I to an ω-limit set W of f . Consequently, any nowhere-dense compact set and any finite union of compact intervals is a homeomorphic copy of an ω-limit set of f .