Vanishing hyperbolic repulsive-point mass conjecture for non-Archimedean rational maps
Vanishing hyperbolic repulsive-point mass conjecture for non-Archimedean rational maps
Fix a rational map over of degree , let be its Lyapunov exponent, let denote the hyperbolic space, and let be the set of repulsive fixed points of . Vanishing hyperbolic repulsive-point mass conjecture. If , then
Together with the preceding equidistribution conjectures, this concerns the asymptotic contribution of repulsive periodic points in the hyperbolic space. The source does not state a general resolution; it records affirmative results in the moderate zero-exponent setting and describes the non-moderate case as delicate.
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Sources & referencesView supporting material
Primary source
Charles Favre and Juan Rivera-Letelier, “Rigidité, expansion et entropie en dynamique non-archimédienne (Rigidity, expansion and entropy in non-Archimedean dynamics)”, arXiv:2504.20280 (2026).
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