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...

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Bibliographic Details
Authors: Zafar, Sundus|||0000-0003-2213-1565, Cimà, Anna|||0000-0003-0256-518X
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
Description
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.