Pseudo-automorphisms with no invariant foliation
Eric Bedford Serge Cantat Kyounghee Kim
Journal of Modern Dynamics 2014, 8(2): 221-250 doi: 10.3934/jmd.2014.8.221
We construct an example of a birational transformation of a rational threefold for which the first and second dynamical degrees coincide and are $>1$, but which does not preserve any holomorphic (singular) foliation. In particular, this provides a negative answer to a question of Guedj. On our way, we develop several techniques to study foliations which are invariant under birational transformations.
keywords: rational 3-folds cohomologically nonhyperbolic dynamical degrees. invariant foliation regular birational map singular foliation Pseudo-automorphism

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