Hierarchy of Chaotic Maps with an Invariant Measure

Abstract

We give hierarchy of one-parameter family F(a,x) of maps of the interval [0,1] with an invariant measure. 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-parameter family of maps such as logistic and tent maps, these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor at certain parameter 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.

18 pages (Latex), 7 figures

References in corpus (3)

• Random perturbations of chaotic dynamical systems. Stability of the spectrum
• An Analytical Construction of the SRB Measures for Baker-type Maps
• Field Driven Thermostated System : A Non-Linear Multi-Baker Map

Cited by in corpus (4)

• 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