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On variants of distributional chaos in dimension one

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F11%3A%230000301" target="_blank" >RIV/47813059:19610/11:#0000301 - isvavai.cz</a>

  • Result on the web

    <a href="http://www.tandfonline.com/doi/abs/10.1080/14689367.2011.588199" target="_blank" >http://www.tandfonline.com/doi/abs/10.1080/14689367.2011.588199</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1080/14689367.2011.588199" target="_blank" >10.1080/14689367.2011.588199</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On variants of distributional chaos in dimension one

  • Original language description

    In their famous paper from 1994, B. Schwaizer and J. Smital, [B. Schwaizer and J. Smital, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc. 344 (1994), pp. 737-754] fully characterized topological entropy of interval maps in terms of distribution functions of distance between trajectories. Strictly speaking, they proved that a continuous map f :[0, 1]->[0, 1] has zero topological entropy if and only if for every x, y is an element of [0, 1] thefollowing limit exists: lim(n -> infinity) 1/n vertical bar{0 <= i < n : d (f(i)(x),f(i)(y)) < t}vertical bar for every real number t except at most countable set. While many partial efforts have been made in previous years, still there is no proof thatthe result of Schwaizer and Smital holds on every topological graph. Here we offer the proof of this fact, filling a gap existing in the literature of the topic.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • Continuities

    Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2011

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Dynamical Systems: An International Journal

  • ISSN

    1468-9367

  • e-ISSN

  • Volume of the periodical

    26

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    13

  • Pages from-to

    273-285

  • UT code for WoS article

    000299632100004

  • EID of the result in the Scopus database