On the Relation between the Average Complexity Oftrajectorries and the Complexity for Z^n Actions
[1]
Bünyamin AYDIN , Faculty of Education, Konya NecmettinErbakan University Konya TURKEY.
[2]
Ayşe YAŞAR YAVUZ , Faculty of Education, Konya NecmettinErbakan University Konya TURKEY.
The complexity of finite object was introduced by A. Kolmogorov and V. Tihomirov in ([2], [14], [16]) and it was conjectured that for Z actions complexity coincides with topological entropy, ([3], [13], [15]). In the present paper we introduce complexity for Z^n actions and prove the Kolmogorov assertion for continuous actions of Z^n([2], [4]). After, We will examine the relation between the average complexity of trajectories and the complexity for Z^nactions.
Dynamical System, Configuration Spaces, Complexity, Topological Entropy, Measure-Preserving Transformations, Algorithmic, Convergence Rates
[1]
Alekseev V. Symbolic dynamics Institute of Mathematics, Academy Science of Ukraine, Kiev, 1976,225 p.(in Russian)
[2]
A. Komogorov and V. Tihomirov. "s-Entropy and s-Capacity of Sets in Function Spaces", Uspehi. Math., Nauk 14, No:2(86),English transl., Amer. Soc.,Tarns.,1996
[3]
A M. Stepin and AT. Tagi-Zade, "Combinatoriallnterpretations of the entropy Symbolic Systems", Math. Note.v46. N3.,653-658,1989
[4]
Aydın, B. " Entropy and The Complexity for ZN actions" ISSN 1392-124X Informacınes TechnologıjosIr Valdymas, 2004,Nr.2(31)
[5]
Brudno A On the complexity of dynamical systems trajectories, Uspekhi math nauk, 1978,v.33(1 ),pp.207-208 (in Russian)
[6]
Brudno A Metric and topological characteristics of individual trajectories of dynamical system, Ph. D.thesis, Moscov, 1978,(in Russian)
[7]
F. Blume "On the relatıon between entropy and the average complexity of trajectories ın dynamical systems" comput. complex.9(2000), 146-155
[8]
F. Blume The rate of entropy convergence. Doctoral dissertation, University of North Carolina at Chapel Hill 1995
[9]
F. Blume Possible rates of entropy convergence. Ergodic Theory Dnam. Systems 17,45-70,1997
[10]
F. Blume Minimal rates of entropy convergence for completely ergodic systems. Israel J.Math.1 088, 1-12.1998
[11]
F. Blume Minimal rates of entropy convergence for rank one systems. Discerete Contin. Dynam. Systems 6,773-796.2000
[12]
H.S. White. On the algoritmic complexity of the trajectories of points in dynamical systems. Doctoral dissertation, University of North Carolina at Chapel HiII.(1991)
[13]
Kolmogoran A. Three approaches to the definition of the definition of notion of information quantity, problems of information transferring, v.5, number3, 1965, pp.3-7 (in Russian)
[14]
L. Levin. Univesal Sorting problems. Problemy Peredaci Informacii, (in Russian) English Trans. In Problems of Information Transmission, 9,1973,265-266.
[15]
Ornstein D.S., Weiss B. Entropy and isomorphism theorems for actions of amenable group, Ann. of Mathematics, 1987,v.3,pp.3-257
[16]
R. Caldebank (Ed),"Different Aspects of Coding Theory", Amer. Math. Soc. Short Cours., January2-3,San Francisco, California,1995.
[17]
StepinA, Tagi-zade A Variational characterization of topological pressure of amenabel group actions. Docl. Academy Nauk of USSR.1980,V.254,number3,pp.545-549 (in Russian)
[18]
Tagi-zade A, Kuliev T. On the complexity of symbolic system on nonabeliangroups, linear operators and its applications, Baku, 1984,pp.1 05-11 O(in Russian)
[19]
Tempelman A. Ergodic theorems on groups Vilnus,1986,224p., ( in Russian)
