On one-sided, D-chaotic CA without fixed points, having continuum of periodic points with period 2 and topological entropy log(p) for any prime p

Wit Foryś; Janusz Matyja

doi:10.3390/e16115601

On one-sided, D-chaotic CA without fixed points, having continuum of periodic points with period 2 and topological entropy log(p) for any prime p

Wit Foryś
, Janusz Matyja

Department of Economy and Informatics (ROZ/ROZ1)

Jagiellonian University in Kraków

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

A method is known by which any integer n ≥ 2 in a metric Cantor space of right-infinite words Ã^N_n gives a construction of a non-injective cellular automaton (Ã^N_n , F_n), which is chaotic in Devaney sense, has a radius r = 1, continuum of fixed points and topological entropy log(n): As a generalization of this method we present for any integer n ≥ 2, a construction of a cellular automaton (A^N_n , F_n); which has the listed properties of (Ã^N_n , F_n), but has no fixed points and has continuum of periodic points with the period 2. The construction is based on properties of cellular automaton introduced here (B^N, F) with radius 1 defined for any prime number p: We prove that (B^N, F) is non-injective, chaotic in Devaney sense, has no fixed points, has continuum of periodic points with the period 2 and topological entropy log(p).

Original language	English
Pages (from-to)	5601-5617
Number of pages	17
Journal	Entropy
Volume	16
Issue number	11
DOIs	https://doi.org/10.3390/e16115601
Publication status	Published - 2014

Keywords

D-chaotic
E-chaotic
Fixed points
One-sided cellular automata
Topological entropy

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.3390/e16115601

Cite this

@article{79b4f06403cd4db388583249cc869d09,

title = "On one-sided, D-chaotic CA without fixed points, having continuum of periodic points with period 2 and topological entropy log(p) for any prime p",

abstract = "A method is known by which any integer n ≥ 2 in a metric Cantor space of right-infinite words {\~A}Nn gives a construction of a non-injective cellular automaton ({\~A}Nn , Fn), which is chaotic in Devaney sense, has a radius r = 1, continuum of fixed points and topological entropy log(n): As a generalization of this method we present for any integer n ≥ 2, a construction of a cellular automaton (ANn , Fn); which has the listed properties of ({\~A}Nn , Fn), but has no fixed points and has continuum of periodic points with the period 2. The construction is based on properties of cellular automaton introduced here (BN, F) with radius 1 defined for any prime number p: We prove that (BN, F) is non-injective, chaotic in Devaney sense, has no fixed points, has continuum of periodic points with the period 2 and topological entropy log(p).",

keywords = "D-chaotic, E-chaotic, Fixed points, One-sided cellular automata, Topological entropy",

author = "Wit Fory{\'s} and Janusz Matyja",

note = "Publisher Copyright: {\textcopyright} 2014 by the authors.",

year = "2014",

doi = "10.3390/e16115601",

language = "English",

volume = "16",

pages = "5601--5617",

journal = "Entropy",

issn = "1099-4300",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "11",

}

TY - JOUR

T1 - On one-sided, D-chaotic CA without fixed points, having continuum of periodic points with period 2 and topological entropy log(p) for any prime p

AU - Foryś, Wit

AU - Matyja, Janusz

PY - 2014

Y1 - 2014

N2 - A method is known by which any integer n ≥ 2 in a metric Cantor space of right-infinite words ÃNn gives a construction of a non-injective cellular automaton (ÃNn , Fn), which is chaotic in Devaney sense, has a radius r = 1, continuum of fixed points and topological entropy log(n): As a generalization of this method we present for any integer n ≥ 2, a construction of a cellular automaton (ANn , Fn); which has the listed properties of (ÃNn , Fn), but has no fixed points and has continuum of periodic points with the period 2. The construction is based on properties of cellular automaton introduced here (BN, F) with radius 1 defined for any prime number p: We prove that (BN, F) is non-injective, chaotic in Devaney sense, has no fixed points, has continuum of periodic points with the period 2 and topological entropy log(p).

AB - A method is known by which any integer n ≥ 2 in a metric Cantor space of right-infinite words ÃNn gives a construction of a non-injective cellular automaton (ÃNn , Fn), which is chaotic in Devaney sense, has a radius r = 1, continuum of fixed points and topological entropy log(n): As a generalization of this method we present for any integer n ≥ 2, a construction of a cellular automaton (ANn , Fn); which has the listed properties of (ÃNn , Fn), but has no fixed points and has continuum of periodic points with the period 2. The construction is based on properties of cellular automaton introduced here (BN, F) with radius 1 defined for any prime number p: We prove that (BN, F) is non-injective, chaotic in Devaney sense, has no fixed points, has continuum of periodic points with the period 2 and topological entropy log(p).

KW - D-chaotic

KW - E-chaotic

KW - Fixed points

KW - One-sided cellular automata

KW - Topological entropy

UR - https://www.scopus.com/pages/publications/84911892519

U2 - 10.3390/e16115601

DO - 10.3390/e16115601

M3 - Article

AN - SCOPUS:84911892519

SN - 1099-4300

VL - 16

SP - 5601

EP - 5617

JO - Entropy

JF - Entropy

IS - 11

ER -

On one-sided, D-chaotic CA without fixed points, having continuum of periodic points with period 2 and topological entropy log(p) for any prime p

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this