On complete chaotic maps with tent-map-like structures. (English) Zbl 1064.37029

Summary: A unimodal map \(f : [0, 1]\to [0, 1]\) is said to be complete chaotic if it is both ergodic and chaotic in a probabilistic sense so as to preserve an absolutely continuous invariant measure. Sufficient conditions are provided to construct complete chaotic maps with the tent-map-like structures, that is, \(f(x) = 1 - |1 - 2g(x)|\), where \(g\) is a one-to-one onto map defined on \([0, 1]\). The simplicity and analytical characteristics of such chaotic maps simplify the calculations of various statistical properties of chaotic dynamics.


37E05 Dynamical systems involving maps of the interval
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
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