A BSTRACT. We study causes of stretching of Birkhoff sums and study their action in the mixing of various surface flows. In so doing, we succeed in amplifying the result of Khanin and Sinai about mixing in the Arnold’s

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• Stochastic processes
• Statistics
• Mathematics
• Ergodicity
• Probability theory
• Mixing
• Irrational rotation
• Measure-preserving dynamical system
• Continuous function
• Mathematical analysis
• Ergodic theory
• Dynamical systems