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Foliations and conjugacy: Anosov structures in the plane

Published online by Cambridge University Press:  14 March 2014

JORGE GROISMAN  and
ZBIGNIEW NITECKI
JORGE GROISMAN
Affiliation:
Instituto de Matemática y Estadística Prof. Ing. Rafael Laguardia, Facultad de Ingeniería Julio Herrera y Reissig 565 11300, Montevideo, Uruguay email [email protected]
ZBIGNIEW NITECKI
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, USA email [email protected]
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Abstract

In a non-compact setting, the notion of hyperbolicity, together with the associated structure of stable and unstable manifolds (for unbounded orbits), is highly dependent on the choice of metric used to define it. We consider the simplest version of this, the analogue for the plane of Anosov diffeomorphisms, studied earlier by White and Mendes. The two known topological conjugacy classes of such diffeomorphisms are linear hyperbolic automorphisms and translations. We show that if the structure of stable and unstable manifolds is required to be preserved by these conjugacies, the number of distinct equivalence classes of Anosov diffeomorphisms in the plane becomes infinite.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 4 , June 2015 , pp. 1229 - 1242
Copyright
© Cambridge University Press, 2014 

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References

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