A nonlinear dynamics perspective of wolfram's new kind of science. Part ix: Quasi-ergodicity

International Journal of Bifurcation and Chaos

Volumn 18, Issue 9, 2008, Pages 2487-2642

  Chua, Leon O ^a   Pazienza, Giovanni Egidio ^b   Orzo, Laszlo ^c   Sbitnev, Valery I ^d   Shin, Jinwook ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITAT RAMON LLULL   (Spain)

^c INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^d PETERSBURG NUCLEAR PHYSICS INSTITUTE   (Russian Federation)

Author keywords

Attractors; Basin tree diagram; Bernoulli return time; Bernoulli shift; Bernoulli velocity; Binomial series; Cellular automata; Complex Bernoulli shifts; Ergodicity; Hyper Bernoulli shifts; Isles of Eden; Nonlinear dynamics; Quasi ergodicity; Shift maps

Indexed keywords

CELLULAR AUTOMATA; FORESTRY; FRACTALS;

ATTRACTORS; BASIN TREE DIAGRAM; BERNOULLI RETURN TIME; BERNOULLI SHIFT; BERNOULLI VELOCITY; BINOMIAL SERIES; COMPLEX BERNOULLI SHIFTS; ERGODICITY; HYPER BERNOULLI SHIFTS; ISLES OF EDEN; QUASI-ERGODICITY; SHIFT MAPS;

DYNAMICS;

EID: 57249107866     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127408021853     Document Type: Review

References (23)

1. Cattaneo, G. & Quaranta Vogliotti, C. [1997] "The 'magic' rule spaces of neural-like elementary cellular automata", Theoret. Comput. Sci. 178, 77-102.
2. Chua, L. O. [1996] CNN: A Paradigm for Complexity (World Scientific, Singapore).
3. Chua, L. O., Yoon, S. & Dogaru, R. [2002] "A nonlinear dynamics perspective of Wolfram's new kind of science. Part I: Threshold of complexity", Int. J. Bifurcation and Chaos 13, 2377-2491.
4. Chua, L. O., Sbitnev, V. I. & Yoon, S. [2003] "A nonlinear dynamics perspective of Wolfram's new kind of science. Part II: Universal neuron", Int. J. Bifurcation and Chaos 13, 2377-2491.
5. Chua, L. O., Sbitnev, V. I. & Yoon, S. [2004] "A nonlinear dynamics perspective of Wolfram's new kind of science. Part III: Predicting the unpredictable", Int. J. Bifurcation and Chaos 14, 3689-3820.
6. Chua, L. O., Sbitnev, V. I. & Yoon, S. [2005a] "A nonlinear dynamics perspective of Wolfram's new kind of science. Part IV: From Bernoulli shift to 1/f spectrum", Int. J. Bifurcation and Chaos 15, 1045-1183.
7. Chua, L. O., Sbitnev, V. I. & Yoon, S. [2005b] "A nonlinear dynamics perspective of Wolfram's new kind of science. Part V: Fractals everywhere", Int. J. Bifurcation and Chaos 15, 3701-3849.
8. Chua, L. O., Sbitnev, V. T. & Yoon, S. [2006] "A nonlinear dynamics perspective of Wolfram's new kind of science. Part VI: From time-reversible attractors to the arrow of time", Int. J. Bifurcation and Chaos 18, 1097-1373.
9. Chua, L. O., Guan, J., Sbitnev, V. I. & Jinwook, S. [2007a] "A nonlinear dynamics perspective of Wolfram's new kind of science. Part VII: Isles of Eden", Int. J. Bifurcation and Chaos 17, 2839-3012.
10. Chua, L. O., Karacs, K., Sbitnev, V. I., Guan, J. & Jinwook, S. [2007b] "A nonlinear dynamics perspective of Wolfram's new kind of science. Part VIII: More Isles of Eden", Int. J. Bifurcation and Chaos 17, 3741-3894.
11. Courbage, M., Mercier, D. & Yasmineh, S. [1999] "Travelling waves and chaotic properties in cellular automata", Chaos 9, 893-901.
12. Courbage, M. & Yasmineh, S. [2001] "Wavelengths distribution of chaotic travelling waves in some cellular automata", Physica D 150, 63-83.
13. d", Int. J. Bifurcation and Chaos 18(10), in press.
14. Hedlund, G. A. [1969] "Endomorphisms and automorphisms of the shift dynamical system", Th. Comput. Syst. 3, 320-375.
15. Ireland, K. & Rosen, M. [1990] A Classical Introduction to Modern Number Theory (Springer-Verlag).
16. Martin, O., Odlyzko, A. M. k Wolfram, S. [1984] "Algebraic properties of cellular automata", Commun. Math. Phys. 93, 219-258.
17. Moore, E. F. [1982] "Machine models of selfreproduction", Proc. Symp. Appl. Math. 14, 17-33.
18. Myhill, J. [1963] "The converse of Moore's Garden-of- Eden theorem", Proc. Arner. Math. Soc. 14, 685-686.
19. Ohi, F. [2007] "Chaotic properties of the elementary cellular automaton rule 40 in Wolfram's class I", Compl. Syst. 17, 295-308.
20. Pivato, M. & Yassami, R. [2008] "The spatial structure of odometers in certain cellular automata", Journ'ees Automates Cellulaires 1, 119-126.
21. Shereshevsky, M. A. [1992] "Ergodic properties of certain surjective cellular automata", Mh. Math. 114, 305-316.
22. Shirvani, M. & Rogers, T. D. [1991] "On ergodic one-dimensional cellular automata", Commun. Math. Phys. 138, 599-605.
23. Wuensche, A. & Lesser, M. [1992] The Global Dynamics of Cellular Automata: An Atlas of Basin of Attraction Fields of One-Dimensional Cellular Automata (Addison-Wesley, Reading, MA).