Abstract
The logarithmic map given by the difference equation xx +1 = ln ( a | xn |) generates chaos for e-1 ≪ a ≪ e . The variation of xn in n -sequence of a chaos region represents characteristic shapes depending on parameter a . The entropy and Lyapunov exponent for the system are obtained as a function of a . On repeating transformation for the case a = 1.0 by which a point stretched unlimitedly by this dynamical equation is squeezed in the region (0, 1), a fractal behaviour characterized by self-affinity can be found in the expansion of the n -sequence for various initial values x0 .
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