## 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.

### MSC:

 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

### Keywords:

unimodal map; invariant measure; chaotic maps
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### References:

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