Ergodic properties of fibered rational maps

Mattias Jonsson

doi:10.1007/BF02384321

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Home > Journals > Ark. Mat. > Volume 38 > Issue 2 > Article

October 2000 Ergodic properties of fibered rational maps

Mattias Jonsson

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Mattias Jonsson¹
¹Department of Mathematics, University of Michigan

Ark. Mat. 38(2): 281-317 (October 2000). DOI: 10.1007/BF02384321

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Abstract

We study the ergodic properties of fibered rational maps of the Riemann sphere. In particular we compute the topological entropy of such mappings and construct a measure of maximal relative entropy. The measure is shown to be the unique one with this property. We apply the results to selfmaps of ruled surfaces and to certain holomorphic mapping of the complex projective plane P².