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

Bessa, Mário; Rocha, Jorge

http://hdl.handle.net/10400.2/13828

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Authors

Bessa, Mário

Rocha, Jorge

Abstract(s)

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 Hénon 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 Hénon map to a translation.

Keywords

Free maps of the plane Hénon map Area-preserving maps Topological conjugacy Fundamental regions

URI

http://hdl.handle.net/10400.2/13828

Citation

Bessa, M., & Rocha, J. (2008). On the fundamental regions of a fixed point free conservative Hénon map. Bulletin of the Australian Mathematical Society, 77(1), 37-48.