Abstract
We study a simple dynamical system which displays a so-called “type-I intermittency” bifurcation. We determine the Bowen-Ruelle measure με and prove that the expectation με(g) of any continuous functiong and the Kolmogoroff-Sinai entropyh(με) are continuous functions of the bifurcation parameterɛ. Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.
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Meunier, C. Continuity of type-I intermittency from a measure-theoretical point of view. J Stat Phys 36, 321–365 (1984). https://doi.org/10.1007/BF01010987
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DOI: https://doi.org/10.1007/BF01010987