Geometry and ergodic theory of parabolic meromorphic functions. (English) Zbl 1497.30010
Summary: Let \(f\) be a parabolic transcendental meromorphic function with positive and finite order \(\rho\) and its derivative satisfies some growth conditions. In this paper, we show the existence of conformal measures and use this basic tool to illustrate both geometrical and dynamical features of the radial Julia set. We also characterize the conformal measures supported on radial Julia sets.
MSC:
| 30D30 | Meromorphic functions of one complex variable (general theory) |
| 37F10 | Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets |
| 30C85 | Capacity and harmonic measure in the complex plane |
Keywords:
parabolic meromorphic function; Perron-Frobenius operator; pressure functions; conformal measuresReferences:
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