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Dimension and invertibility of hyperbolic endomorphisms with singularities

Published online by Cambridge University Press:  01 October 1998

J. SCHMELING  and
S. TROUBETZKOY
J. SCHMELING
Affiliation:
Freie Universitaet Berlin, Fachbereich fuer Mathematik und Informatik, Arnimallee 2–6, 14975 Berlin, Germany (e-mail: shmeling@math.fu-berlin.de)
S. TROUBETZKOY
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA (e-mail: troubetz@math.uab.edu)
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Abstract

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We introduce and study a class of endomorphisms which are piecewise smooth and have hyperbolic attractors. We prove the existence of SBR measures and develop the stable manifold theory and ergodic theory of such maps. We show that the Young dimension formula holds if and only if the map is invertible SBR-almost everywhere.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 5 , October 1998 , pp. 1257 - 1282
Copyright
© 1998 Cambridge University Press