Composition of Chaotic Maps with an Invariant Measure

Abstract

We generate new hierarchy of many-parameter family of maps of the interval [0,1] with an invariant measure, by composition of the chaotic maps of reference [1]. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of these maps analytically, where the results thus obtained have been approved with numerical simulation. In contrary to the usual one-dimensional maps and similar to the maps of reference [1], these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor at certain region of parameters values, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at these values of parameter whose Lyapunov characteristic exponent begins to be positive.

20 Pages, 8 Figures

References in corpus (2)

• Random perturbations of chaotic dynamical systems. Stability of the spectrum
• An Analytical Construction of the SRB Measures for Baker-type Maps

Cited by in corpus (5)

• Applications of tripled chaotic maps in cryptography
• Hierarchy of one and many-parameter families of elliptic chaotic maps of cn and sn types
• Hierarchy of piecewise non-linear maps with non-ergodicity behavior
• Hierarchy of random deterministic chaotic maps with an invariant measure
• Chaos suppression via adaptive feedback control of intermittency: From exactly solvable ergodic maps to interacting microbubble clusters