Abstract
This work dynamically classifies a 9-parametric family of birational maps \(f: {\mathbb {C}}^2 \rightarrow {\mathbb {C}}^2\). From the sequence of the degrees \(d_n\) of the iterates of f, we find the dynamical degree \(\delta (f)\) of f. We identify when \(d_n\) grows periodically, linearly, quadratically or exponentially. The considered family includes the birational maps studied by Bedford and Kim (Mich Math J 54:647–670, 2006) as one of its subfamilies.
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Acknowledgements
The first author is supported by Ministry of Economy, Industry and Competitiveness of the Spanish Government through Grants MINECO/FEDER MTM2016-77278 and also supported by the grant 2017-SGR-1617 from AGAUR, Generalitat de Catalunya.
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Zafar, S., Cima, A. Dynamical Classification of a Family of Birational Maps of \({\mathbb {C}}^2\) via Algebraic Entropy. Qual. Theory Dyn. Syst. 18, 631–652 (2019). https://doi.org/10.1007/s12346-018-0304-1
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DOI: https://doi.org/10.1007/s12346-018-0304-1