Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Atomic disintegrations for partially hyperbolic diffeomorphisms


Author: Ale Jan Homburg
Journal: Proc. Amer. Math. Soc. 145 (2017), 2981-2996
MSC (2010): Primary 37C05, 37D30
DOI: https://doi.org/10.1090/proc/13509
Published electronically: January 6, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Shub and Wilkinson and Ruelle and Wilkinson studied a class of volume preserving diffeomorphisms on the three dimensional torus that are stably ergodic. The diffeomorphisms are partially hyperbolic and admit an invariant central foliation of circles. The foliation is not absolutely continuous; in fact, Ruelle and Wilkinson established that the disintegration of volume along central leaves is atomic. We show that in such a class of volume preserving diffeomorphisms the disintegration of volume along central leaves is a single delta measure. We also formulate a general result for conservative three dimensional skew product like diffeomorphisms on circle bundles, providing conditions for delta measures as disintegrations of the smooth invariant measure.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37C05, 37D30

Retrieve articles in all journals with MSC (2010): 37C05, 37D30


Additional Information

Ale Jan Homburg
Affiliation: KdV Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands – and – Department of Mathematics, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
Email: a.j.homburg@uva.nl

DOI: https://doi.org/10.1090/proc/13509
Received by editor(s): September 29, 2015
Received by editor(s) in revised form: March 7, 2016, and August 8, 2016
Published electronically: January 6, 2017
Communicated by: Nimish Shah
Article copyright: © Copyright 2017 American Mathematical Society