Invariant fibrations for some birational maps of ℂ₂

Abstract

In this article, we extract and study the zero entropy subfamilies of a certain family of birational maps of the plane. We find these zero entropy mappings and give the invariant fibrations associated to them.

Keywords:

• Birational maps
• algebraic entropy
• first integrals
• fibrations
• blowing-up
• integrability
• periodicity

Mathematics Subject Classification 2010:

• 14E05
• 26C15
• 28D20
• 34K19
• 37C15
• 39A23

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Sundus Zafar http://orcid.org/0000-0003-2213-1565

Additional information

Funding

The first author is supported by Ministry of Economy, Industry and Competitiveness of the Spanish Government through grant MINECO/FEDER MTM2016-77278-P and also by the grant 2017-SGR-1617 from AGAUR, Generalitat de Catalunya.