Dynamical classification of a family of birational maps of C2 via algebraic entropy
This work dynamically classifies a 9-parametric family of birational maps f: C→ C. From the sequence of the degrees d of the iterates of f, we find the dynamical degree δ(f) of f. We identify when d grows periodically, linearly, quadratically or exponentially. The considered family includes the bira...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:221374 |
| Online Access: | https://ddd.uab.cat/record/221374 https://dx.doi.org/urn:doi:10.1007/s12346-018-0304-1 |
| Access Level: | Open access |
| Keyword: | Birational maps Algebraic entropy First Integrals Fibrations Blowing-up Integrability Periodicity Chaos |
| Summary: | This work dynamically classifies a 9-parametric family of birational maps f: C→ C. From the sequence of the degrees d of the iterates of f, we find the dynamical degree δ(f) of f. We identify when d 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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