Jafarizadeh, M. A.; Behnia, S.; Khorram, S.; Nagshara, H. Hierarchy of chaotic maps with an invariant measure. (English) Zbl 1143.82308 J. Stat. Phys. 104, No. 5-6, 1013-1028 (2001). Summary: We give hierarchy of one-parameter family \((\alpha, x)\) of maps at 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 the 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 for certain values of the parameter, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at those values of the parameter whose Lyapunov characteristic exponent begins to be positive. Cited in 1 ReviewCited in 18 Documents MSC: 82C05 Classical dynamic and nonequilibrium statistical mechanics (general) 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:chaos; invariant measure; entropy; Lyapunov characteristic exponent; ergodic dynamical systems PDFBibTeX XMLCite \textit{M. A. Jafarizadeh} et al., J. Stat. Phys. 104, No. 5--6, 1013--1028 (2001; Zbl 1143.82308) Full Text: DOI arXiv