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Register a new userStatistical properties of periodic points for infinitely renormalizable unimodal maps
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Hiroki Takahasi
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For an infinitely renormalizable negative Schwarzian unimodal map $f$ with non-flat critical point, we analyze statistical properties of periodic points as the periods tend to infinity. Introducing a weight function $varphi$ which is a continuous or a geometric potential $varphi=-betalog|f|$ ($betainmathbb R$), we establish the level-2 Large Deviation Principle for weighted periodic points. From this, we deduce that all weighted periodic points equidistribute with respect to equilibrium states for the potential $varphi$. In particular, it follows that all periodic points are equidistributed with respect to measures of maximal entropy, and all periodic points weighted with their Lyapunov exponents are equidistributed with respect to the post-critical measure supported on the attracting Cantor set.
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