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• W2045209186 abstract "For any proper polynomial map f: Ck→Ck define the function α as $alpha (z): = mathop {lim sup }limits_{n to infty } frac{{log ^ + log ^ + left| {f^n (z)} right|}}{n},where log^ + : = max { log , 0} .$ Let f=(P1,..., Pk) be a proper polynomial map. We define a notion of s-regularity using the extension of f to Pk. When f is (maximally) regular we show that the function α is lower semicontinuous and takes only finitely many values: 0 and d1,..., dk, where di:=degPi. We then describe dynamically the sets {α≤di}. We give a concrete description of regular maps. If di >1, this allows us to construct the equilibrium measure μ associated with f as a generalized intersection of positive currents. We then give an estimate of the Hausdorff dimension of μ. We extend the approach to the larger class of (π, s)-regular maps. This gives an understanding of the largest values of α. The results can be applied to construct dynamically interesting measures for automorphisms." @default.
• W2045209186 created "2016-06-24" @default.
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• W2045209186 date "2004-04-01" @default.
• W2045209186 modified "2023-09-26" @default.
• W2045209186 title "Dynamique des applications polynomiales semi-régulières" @default.
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• W2045209186 doi "https://doi.org/10.1007/bf02432910" @default.
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