Families, filters and chaos

Oprocha, Piotr
August 2010
Bulletin of the London Mathematical Society;Aug2010, Vol. 42 Issue 4, p713
Academic Journal
In this paper, we use the definition of (ℱ1, ℱ2)-chaos introduced recently by Tan and Xiong together with the properties of residual relations as a tool in construction of various kinds of scrambled sets. In particular, we show that a continuous map acting on a compact metric space has an ɛ-scrambled set if and only if it has a distributionally ɛ-scrambled set with respect to a sequence. We also provide an example of a topologically mixing map with positive topological entropy but without DC1 pairs.


Related Articles

  • TOPOLOGICAL ENTROPY AND DISTRIBUTIONAL CHAOS. Smítal, Jaroslav // Real Analysis Exchange;Jun2006 Conference, Vol. 32, p61 

    The article examines whether there are implications between positive topological entropy and distributional chaos versions DC2 or DC3. It cites the introduction of the notion of distributional chaos for continuous maps of the interval [9] in 1994. It states that the three versions of...

  • A variational principle for topological pressure for certain non-compact sets. Thompson, Daniel // Journal of the London Mathematical Society;Dec2009, Vol. 80 Issue 3, p585 

    Let (X, d) be a compact metric space, let f:X ↦ X be a continuous map with the specification property and let ϕ: X ↦ ℝ be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non-compact sets of the form...

  • Rectifiability of metric flat chains and fractional masses. Stepanov, E. // Journal of Mathematical Sciences;Jun2010, Vol. 167 Issue 3, p406 

    We prove that every real flat chain T of finite mass in a complete separable metric space E is rectifiable when $$ {\mathbb{M}^\alpha }(T) < + \infty $$ for some a ? [0, 1), where $$ {\mathbb{M}^\alpha }(T) $$ is the a-mass of T. Bibliography: 12 titles.

  • A common fixed point theorem for compatible mappings in fuzzy metric spaces using implicit relation. �ikic-Do�enovic, T. // Acta Mathematica Hungarica;Dec2009, Vol. 125 Issue 4, p357 

    Using the theory of countable extension of t-norm we prove a common fixed point theorem for compatible mappings satisfying an implicit relation in fuzzy metric spaces.

  • The Vlasov Limit for a System of Particles which Interact with a Wave Field. Elskens, Y.; Kiessling, M.; Ricci, V. // Communications in Mathematical Physics;Jan2009, Vol. 285 Issue 2, p673 

    A. Komech, M. Kunze and H. Spohn have studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body version of this model is studied and its Vlasov continuum limit...

  • The metric of anti-Thorpe spaces, n = 4k, k > 1. Kim, J. M. // Acta Mathematica Hungarica;2003, Vol. 100 Issue 4, p265 

    We show that in dimension 8, a semiflat metric is flat and that in dimension (8k+4) higher than 8, a semiflat metric does not necessarily imply flat.

  • Finite quasihypermetric spaces. NICKOLAS, P.; WOLF, R. // Acta Mathematica Hungarica;Sep2009, Vol. 124 Issue 3, p243 

    Let ( X, d) be a compact metric space and let $$ \mathcal{M} $$( X) denote the space of all finite signed Borel measures on X. Define I: $$ \mathcal{M} $$( X) ? R by I(�) = ? X? X d( x, y) d�(x)d�( y), and set M( X) = sup I(�), where � ranges over the collection of...

  • K-Theory of Localization Algebras over Discrete Metric Spaces. Qin Wang; Jinxiu Li // Southeast Asian Bulletin of Mathematics;2003, Vol. 27 Issue 3, p553 

    Localization algebras over metric spaces arose from index theory associated with coarse geometry. Let X be a δ-separated proper metric space for some δ > 0. We compute in this note the K-theory groups of the dual algebra of the localization Roe algebra over X. It turns out that both...

  • New results in G-best approximation in G-metric spaces. Nezhad, A. Dehghan; Mazaheri, H. // Ukrainian Mathematical Journal;Nov2010, Vol. 62 Issue 4, p648 

    The purpose of this paper is to introduce and discuss the concepts of G-best approximation and a -orthogonality in the theory of G-metric spaces. We consider the relationship between these concepts and the dual X and obtain some results on subsets of G-metric spaces similar to normed spaces.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics