A note on stable holonomy between centers

Authors: Keith Burns and Amie Wilkinson

Abstract:
We show that the C^2 hypothesis in the Pugh Shub ergodicity theorem for partially hyperbolic diffeomorphisms can be weakened at the cost of strengthening the center bunching hypothesis. Our results apply to partially hyperbolic diffeomorphisms whose derivatives are only H&"o;lder continuous. This is the same smoothness as required in Pesin theory.


A preliminary version of this article is available in the following formats:

The research in this article was supported by National Science Foundation grant DMS-0408704. Needless to say, any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Authors' addresses:
	Keith  Burns 
	Department of Mathematics
	Northwestern University
	Evanston, IL 60208-2730
        
	
	Amie Wilkinson 
	Department of Mathematics
	Northwestern University
	Evanston, IL 60208-2730
        


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