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Physical measures for certain partially hyperbolic attractors on 3-manifolds

Published online by Cambridge University Press:  08 May 2017

RICARDO T. BORTOLOTTI
RICARDO T. BORTOLOTTI*
Affiliation:
Departamento de Matemática – UFPE, Recife, PE, Brazil email ricardo@dmat.ufpe.br
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Abstract

In this work, we analyze ergodic properties of certain partially hyperbolic attractors whose central direction has a neutral behavior; the main feature is a condition of transversality between the projections of unstable leaves, projecting through the stable foliation. We prove that partial hyperbolic attractors satisfying this condition of transversality, neutrality in the central direction and regularity of the stable foliation admit a finite number of physical measures, coinciding with the ergodic u-Gibbs States, whose union of the basins has full Lebesgue measure. Moreover, we describe the construction of robustly non-hyperbolic attractors satisfying these properties.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 1 , January 2019 , pp. 74 - 104
Copyright
© Cambridge University Press, 2017 

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