Hierarchy of chaotic maps with an invariant measure and their compositions

Abstract

We give a hierarchy of many-parameter families of maps of the interval [0,1] with an invariant measure and using the measure, we calculate Kolmogorov--Sinai entropy of these maps analytically. In contrary to the usual one-dimensional 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 region of parameters space, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at certain values of the parameters.

arxiv version is already official

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 (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