Specification property and distributional chaos almost everywhere

Let f be a continuous map from a compact interval into itself. Continuing the work begun by Schweizer and Smítal [1994], we prove that the restriction of f to any basic set (i.e. any nonsolenoidal, infinite, maximal ω-limit set) satisfies a generalization of the specification property. We apply this generalization to establish several conjectures made in the abovementioned paper, e.g. the fact that distributional chaos is stable.

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Extreme Chaos and Transitivity

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127403007540 ◽

2003 ◽

Vol 13 (07) ◽

pp. 1695-1700 ◽

Cited By ~ 3

Author(s):

Marta Babilonová-Štefánková

Keyword(s):

Topological Entropy ◽

Distributional Chaos ◽

Positive Topological Entropy ◽

Continuous Map ◽

Almost Everywhere ◽

Provided Examples

In the eighties, Misiurewicz, Bruckner and Hu provided examples of functions chaotic in the sense of Li and Yorke almost everywhere. In this paper we show that similar results are true for distributional chaos, introduced in [Schweizer & Smítal, 1994]. In fact, we show that any bitransitive continuous map of the interval is conjugate to a map uniformly distributionally chaotic almost everywhere. Using a result of A. M. Blokh we get as a consequence that for any map f with positive topological entropy there is a k such that fk is semiconjugate to a continuous map uniformly distributionally chaotic almost everywhere, and consequently, chaotic in the sense of Li and Yorke almost everywhere.

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Asymptotic average shadowing property, almost specification property and distributional chaos

Modern Physics Letters B ◽

10.1142/s0217984916500019 ◽

2016 ◽

Vol 30 (03) ◽

pp. 1650001 ◽

Cited By ~ 1

Author(s):

Lidong Wang ◽

Xiang Wang ◽

Fengchun Lei ◽

Heng Liu

Keyword(s):

Dynamical System ◽

Orbit Closure ◽

Shadowing Property ◽

Distributional Chaos ◽

Specification Property ◽

Asymptotic Average Shadowing

It is proved that a nontrivial compact dynamical system with asymptotic average shadowing property (AASP) displays uniformly distributional chaos or distributional chaos in a sequence. Moreover, distributional chaos in a system with AASP can be uniform and dense in the measure center, that is, there is an uncountable uniformly distributionally scrambled set consisting of such points that the orbit closure of every point contains the measure center. As a corollary, the similar results hold for the system with almost specification property.

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The weak specification property and distributional chaos

Nonlinear Analysis ◽

10.1016/j.na.2013.06.007 ◽

2013 ◽

Vol 91 ◽

pp. 46-50 ◽

Cited By ~ 6

Author(s):

Hui Wang ◽

Lidong Wang

Keyword(s):

Distributional Chaos ◽

Specification Property

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Microstructural Characterization of Au-Ge-Ni based ohmic contacts to GaAs/AlGaAs modfet device

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100126433 ◽

1987 ◽

Vol 45 ◽

pp. 326-327

Author(s):

A.K. Rai ◽

A.K. Petford-Long ◽

A. Ezis ◽

D.W. Langer

Keyword(s):

Contact Resistance ◽

Ohmic Contact ◽

Ohmic Contacts ◽

Microstructural Characterization ◽

Almost Everywhere ◽

Spacer Layer ◽

Good Contact ◽

The Relationship ◽

Lower Contact

Considerable amount of work has been done in studying the relationship between the contact resistance and the microstructure of the Au-Ge-Ni based ohmic contacts to n-GaAs. It has been found that the lower contact resistivity is due to the presence of Ge rich and Au free regions (good contact area) in contact with GaAs. Thus in order to obtain an ohmic contact with lower contact resistance one should obtain a uniformly alloyed region of good contact areas almost everywhere. This can possibly be accomplished by utilizing various alloying schemes. In this work microstructural characterization, employing TEM techniques, of the sequentially deposited Au-Ge-Ni based ohmic contact to the MODFET device is presented.The substrate used in the present work consists of 1 μm thick buffer layer of GaAs grown on a semi-insulating GaAs substrate followed by a 25 Å spacer layer of undoped AlGaAs.

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HUBUNGAN HIGIENE SANITASI DENGAN KANDUNGAN ESCHERICHIA COLI PADA ES BATU INDUSTRI RUMAH TANGGA DI TEPI JALAN WAHID HASYIM 2 KECAMATAN SEMPAJA KOTA SAMARINDA TAHUN 2015

KESMAS UWIGAMA: Jurnal Kesehatan Masyarakat ◽

10.24903/kujkm.v2i1.301 ◽

2018 ◽

Vol 2 (1) ◽

pp. 43

Author(s):

Suwignyo Suwignyo ◽

Abdul Rachim ◽

Arizal Sapitri

Keyword(s):

Escherichia Coli ◽

Data Analysis ◽

Random Sampling ◽

Preliminary Test ◽

Raw Material ◽

Almost Everywhere ◽

Ice Cube ◽

Processing And Storage ◽

And Storage ◽

Cluster Random Sampling

Ice is a water that cooled below 0 °C and used for complement in drink. Ice can be found almost everywhere, including in the Wahid Hasyim Sempaja Roadside. From the preliminary test, obtained 5 samples ice cube were contaminated by Escherichia coli. The purpose of this study was to determine relationship between hygiene and sanitation with presence of Eschericia coli in ice cube of home industry at Wahid Hasyim Roadside Samarinda. This research used quantitative with survey methode. The population in this study was all of the seller in 2nd Wahid Hasyim Roadside. Sample was taken by Krejcie and Morgan so the there were 44 samples and used Cluster Random Sampling. The instruments are questionnaries, observation and laboratory test. Data analysis was carried out univariate and bivariate (using Fisher test p= 0.05). The conclusion of this study there are a relation between chosing raw material (p=0,03) and saving raw material (p=0,03) with presence of Eschericia coli. There was no relation between processing raw material into ice cube with presence of Eschericia coli (p=0,15).Advice that can be given to ice cube should maintain hygiene and sanitation of the selection, processing and storage of ice cube.

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