, Volume 38, Issue 2, pp 281-317

Ergodic properties of fibered rational maps

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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 planeP 2.

Supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT).