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

  • MÁRIO BESSA (a1) and JORGE ROCHA (a2)

Abstract

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.

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References

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[2]Dacorogna, B. and Moser, J., ‘On a partial differential equation involving the Jacobian determinant’, Ann. Inst. H. Poincaré Anal. Non. Linéaire 7 (1990), 126.
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ON THE FUNDAMENTAL REGIONS OF A FIXED POINT FREE CONSERVATIVE HÉNON MAP

  • MÁRIO BESSA (a1) and JORGE ROCHA (a2)

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