# Chaos and randomness

## Random dynamical system approaches to Noise-induced phenomena

Kolmogorov-Sinai entropy was introduced interpreting generating entropy of chaotic dynamical systems as Shannon entropy of Markov information source [1]. R. Shaw and colleagues studied information flow in dynamical systems with presence of noise by using a framework of noisy communication channels from past to future [2]. Phenomenology and information theoretic significance of such noised dynamical systems are not well-studied except a few works [3][4]. I am working on noise-induced phenomena arisen from interaction between deterministic chaos and stochastic noise, and in general, complex nonlinear phenomena in random dynamics. Applications to time-series analysis and prediction are also investigated with this framework.

[1] A. N. Kolmogorov,
Dokl. Akad. Nauk. SSSR, 124, p754, (1959); Ya. Sinai,
Dokl. Akad. Nauk. SSSR, 124, p768, (1959).

[2] R. Shaw, "Dripping Faucet as a Model Chaotic System," Ariel Press, (1984);
R. Shaw, Z. Naturforsch, 36a, p80, (1981).

[3] Y. Oono and Y. Takahashi,
Prog. Theor. Phys., 63:5, p1804, (1980);
Y. Takahashi and Y. Oono,
Prog. Theor. Phys., 71:4, p851, (1984);
T. Morita,
J. Math. Soc. Japan, 37(4), p651-663, (1985);
A. Lasota and M.C. Mackey,
Physica, D28, p143-154, (1987);

[4] G. Mayer-Kress and H. Haken,
J. Stat. Phys., 26, p149, (1981);
J. P. Crutchfield, J. D. Farmer and B. A. Huberman,
Phys. Lett., 92:2, p45, (1982);
K. Matsumoto and I. Tsuda,
J. Stat. Phys., 31, p87, (1983).