On the fundamental regions of a fixed point free conservative Henon map

• Type: Article in International Scientific Journal
• Date: 2008

Authors

Mario Bessa (Author) Other; Jorge Rocha (Author) FCUP

Journal

Title: Bulletin of the Australian Mathematical Society

Vol. 77

Pages: 37-48

ISSN: 0004-9727

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-004-1N2

DOI: 10.1017/s000497270800004x

Abstract (EN): It is well known that an orientation-preserving homeomorphism of the plane without fixed points has trivial dynamics; that is, its non-wandering set is empty and all the orbits diverge to infinity. However, orbits can diverge to infinity in many different ways (or not) giving rise to fundamental regions of divergence. Such a map is topologically equivalent to a plane translation if and only if it has only one fundamental region. We consider the conservative, orientation-preserving and fixed point free Henon map and prove that it has only one fundamental region of divergence. Actually, we prove that there exists an area-preserving homeomorphism of the plane that conjugates this Henon map to a translation.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12