Generic area-preserving reversible diffeomorphisms

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Maria Pires de Carvalho (Author) FCUP; Mário Bessa (Author) Other; Alexandre Rodrigues (Author) Other

Journal

Title: Nonlinearity

Vol. 28

Pages: 1695-1720

ISSN: 0951-7715

Publisher: Institute of Physics Publishing

Indexing

ISI Web of Knowledge - 1 Citation

ISI Web of Science

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

CORDIS: Physical sciences > Mathematics

Other information

Authenticus ID: P-00G-4HV

DOI: 10.1088/0951-7715/28/6/1695

Abstract (EN): Let M be a surface and R : M -> M an area-preserving C-infinity diffeomorphism which is an involution and whose set of fixed points is a submanifold with dimension one. We will prove that C-1 - generically either an area-preserving R-reversible diffeomorphism, is Anosov, or, for mu-almost every x is an element of M, the Lyapunov exponents at x vanish or else the orbit of x belongs to a compact hyperbolic set with an empty interior. We will also describe a nonempty C-1-open subset of area-preserving R-reversible diffeomorphisms where for C-1 - generically each map is either Anosov or its Lyapunov exponents vanish from almost everywhere.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 26