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ON THE FUNDAMENTAL REGIONS OF A FIXED POINT FREE CONSERVATIVE HÉNON MAP

Part of: Connections with other structures, applications Measure-theoretic ergodic theory Topological dynamics

Published online by Cambridge University Press:  01 February 2008

MÁRIO BESSA  and
JORGE ROCHA
MÁRIO BESSA
Affiliation:
CMUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal (email: bessa@fc.up.pt)
JORGE ROCHA
Affiliation:
DMP-FCUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal (email: jrocha@fc.up.pt)
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Abstract

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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 planeHénon maparea-preserving mapstopological conjugacyfundamental regions

MSC classification

Secondary: 54H20: Topological dynamics 37B99: None of the above, but in this section 28D05: Measure-preserving transformations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 1 , February 2008 , pp. 37 - 48
Copyright
Copyright © Australian Mathematical Society 2008

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