Lyapunov exponents for one-dimensional cellular automata
Tóm tắt
Từ khóa
Tài liệu tham khảo
V. S. Afraimovich and M. A. Shereshevsky (1990) Cellular automata as dynamical systems,Research Reports in Physics. Nonlinear Waves 3 (ed. by A. V. Gaponov-Grekhov, M. I. Rabinovich and J. Engelbrecht), Springer-Verlag, Berlin 296–300.
R. Bowen (1975)Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math.,470, Springer-Verlag, New York.
M. Brin and A. Katok (1983) On local entropy,Lecture Notes in Math.,470, Springer-Verlag, New York, 30–38.
E. M. Coven and M. Paul (1974) Endomorphisms of irreducible shifts of finite type,Math. Syst. Theory,8, 165–177.
J.-P. Eckmann and D. Ruelle (1985) Ergodic theory of chaos and strange attractors,Rev. Modern Phys.,53, 617–656.
J. M. Greenberg, B. D. Hassard and S. P. Hastings (1978) Pattern formation and periodic structures in systems modelled by reaction-diffusion equation,Bull. Amer. Math. Soc.,84, 1296–1327.
G. A. Hedlund (1969) Endomorphisms and automorphisms of the shift dynamical systems,Math. Syst. Theory.,3, 320–375.
W. Li., N. Packard and C. Langton (1990) Transition phenomena in cellular automata rule space,Physica 45D, 77–94.
D. A. Lind (1984) Applications of ergodic theory and sofic systems to cellular automata,Physica 10D, 36–44.
N. Margolus (1984) Physics-like models of computation,Physica 10D, 81–95.
J. von Neumann (1966)Theory of Self-Reproducing Automata (ed. by A. W. Burks), University of Illinois, Urbana.
M. A. Shereshevsky (1991)Ergodic Properties of Certain Surjective Cellular Automata. University of Warwick, Preprint.
M. Shirvani and T. D. Rogers (1991) On ergodic one-dimensional cellular automata,Commun. Math. Phys.,136, 599–605.
S. Wolfram (1984) Universality and complexity in cellular automata,Physica 10D, 1–35.
S. Wolfram (1985) Twenty problems in the theory of cellular automata,Physica Scripta,9, 1–35.