Chaos

Chaos is ubiquitous. Chaotic motions are unpredictable. Quantifying chaos is a central issue for understanding chaotic phenomena. Experimental evidence and theoretical studies predict some qualitative and quantitative measures for quantifying chaos. In this chapter we discuss some measures such as universal sequence (U-sequence), Lyapunov exponent, renormalization group theory, invariant measure, Poincaré section, for quantifying chaotic motions. On the other hand, there are some universal numbers applicable for particular class of systems, for example, the Feigenbaum number, Golden mean, etc. The Lorenz system is a paradigm of deterministic dissipative chaotic systems. The universality is an important feature in chaotic dynamics.