Dynamical coherence of specially absolutely partially hyperbolic endomorphisms on T2. (12th April 2019)

• Record Type: Journal Article
• Authors: He, Baolin; Shi, Yi; Wang, Xiaodong
• Is Part Of: Nonlinearity. Volume 32:Number 5(2019:May)
• Page Start: 1695
• Page End: 1704
• Publication Date: 2019-04-12
• Subjects: endomorphisms -- partial hyperbolicity -- dynamical coherence -- Reeb components; 37C05 -- 37D30 -- 57R30; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab004d
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we prove that every specially absolutely partially hyperbolic endomorphism f on is dynamically coherent. The key point is that we rule out Reeb components in the unstable foliation of f . Moreover, we exhibit a specially partially hyperbolic endomorphism on, which preserves a Reeb foliation as unstable foliation and is not dynamically coherent.