Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps

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Nice Inducing Schemes and the Thermodynamics of Rational Maps (2008, methodology): “Collet-Eckmann rational maps, as well as maps without recurrent critical points and without parabolic periodic points, satisfy the Topological Collet-Eckmann condition; see [PR98] and also [ PRLS03 , Main Theorem].”
Statistical properties of topological Collet–Eckmann maps (2006, background): “This finishes the proof, as for a complex rational map this last condition is equivalent to the TCE condition [35].”
Distribution of rational maps with a preperiodic critical point (2006, methodology): “We refer to [ PRS ] for (many) other characterizations of the TCE condition and references.”
Equality of pressures for rational functions (2004, methodology): “See also [HH ]a nd [ PRS ].) Consider a continuous path γ ⊂ k j =1 Bj without self-intersections joining z0 and x0.”