Hyperbolic dimension and Poincaré critical exponent of rational maps

Huaibin Li () and Pin Xu ()
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Huaibin Li: Henan University
Pin Xu: Henan University

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 2, 285-294

Abstract: Abstract We study the Poincaré series of rational maps. By investigating the property of conical Julia set and dissipative measure, we prove that the Poincaré critical exponents are equal to the hyperbolic dimensions for a large class of rational maps.

Keywords: Rational map; hyperbolic dimension; Poincaré critical exponent (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0228-5

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