Iteration Problem for Distributional Chaos

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F17%3AA0000015" target="_blank" >RIV/47813059:19610/17:A0000015 - isvavai.cz</a>
Result on the web
<a href="http://www.worldscientific.com/doi/abs/10.1142/S0218127417501838" target="_blank" >http://www.worldscientific.com/doi/abs/10.1142/S0218127417501838</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218127417501838" target="_blank" >10.1142/S0218127417501838</a>

Result language
angličtina
Original language name
Iteration Problem for Distributional Chaos
Original language description
We disprove the conjecture that the existence of a DC3-scrambled pair is preserved under iteration and show that a slightly strengthened definition of distributional chaos of type 3, denoted by DC2(1/2), is iteration invariant, i. e. that f^n is DC2(1/2) if and only if f is. Unlike DC3, DC2(1/2) is also conjugacy invariant and implies Li-Yorke chaos. The definition of DC2(1/2) is the following: a pair is DC2(1/2)-scrambled iff Phi(0) < Phi*(0), where Phi(delta) (resp., Phi*(delta)) is lower (resp., upper) asymptotic density of the set of times k when d(f(k)(x), f(k)(y)) < delta, and both densities are defined at 0 as limits of their values for delta -> 0^+. DC2(1/2) shares similar properties with DC1 and DC2 but it is essentially weaker than DC2.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
—
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
ISSN
0218-1274
e-ISSN
1793-6551
Volume of the periodical
27
Issue of the periodical within the volume
12
Country of publishing house
SG - SINGAPORE
Number of pages
10
Pages from-to
„1750183-1“-„1750183-10“
UT code for WoS article
000418277700011
EID of the result in the Scopus database
2-s2.0-85038415390

Similar results(10)