Abstract
We have introduced a simple family of birational transformations in the complex projective space CP n that are generated by the product of the Hadamard inverse and an (involutive) collineation. We have been able to find the integrable subcases of the model and also interesting cases of transcendental integrability. Beyond these integrable subcases, we have been able to describe the degree growth-complexity of the iteration calculations of these birational mappings. These degree growth-complexities appear to be algebraic numbers. We also obtained some simple conjectures for the growth-complexity degrees of these birational transformations in CP n for arbitrary values of n. For the two-dimensional mappings, an equality between the (degree) growth-complexity and the topological entropy was found and we have given some conjectured closed expressions for the dynamical zeta functions.
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