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On the existence of conformal measures supported on conical points. (English) Zbl 1045.37029

Summary: We prove the existence of a \(t\)-conformal measure supported on conical points for a rational map \(T\) whose critical points in its Julia set are recurrent. In particular, there always exists a \(t\)-conformal measure supported on conical points for the polynomial \(T(z)=z^d+c\).

MSC:

37F35 Conformal densities and Hausdorff dimension for holomorphic dynamical systems
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
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