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• W2963947847 abstract "Let $f:mathbb{CP}^2⇢mathbb{CP}^2$ be a rational map with algebraic and topological degrees both equal to $dgeq 2$. Little is known in general about the ergodic properties of such maps. We show here, however, that for an open set of automorphisms $T:mathbb{CP}^2tomathbb{CP}^2$, the perturbed map $Tcirc f$ admits exactly two ergodic measures of maximal entropy $log d$, one of saddle type and one of repelling type. Neither measure is supported in an algebraic curve, and $f_T$ is 'fully two dimensional' in the sense that it does not preserve any singular holomorphic foliation of $mathbb{C}mathbb{P}^2$. In fact, absence of an invariant foliation extends to all $T$ outside a countable union of algebraic subsets of $Aut(mathbb{P}^2)$. Finally, we illustrate all of our results in a more concrete particular instance connected with a two dimensional version of the well-known quadratic Chebyshev map." @default.
• W2963947847 created "2019-07-30" @default.
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• W2963947847 date "2016-08-01" @default.
• W2963947847 modified "2023-09-26" @default.
• W2963947847 title "Typical dynamics of plane rational maps with equal degrees" @default.
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• W2963947847 doi "https://doi.org/10.3934/jmd.2016.10.353" @default.
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