 

Henk Bruin and Jane Hawkins
Rigidity of smooth onesided Bernoulli endomorphisms


Published: 
October 31, 2009

Keywords: 
Bernoulli shifts, onesided Bernoulli, noninvertible maps, interval maps, rational maps 
Subject: 
37A05, 37A10, 37C40, 37E05 


Abstract
A measurepreserving endomorphism is onesided Bernoulli if
it is isomorphic to a noninvertible Bernoulli shift. We show that in
piecewise smooth settings this property is very strong and far more
subtle than the weak Bernoulli property, by extending of results of
W. Parry and P. Walters and proving new results based on continuity
of the RadonNikodym derivative. In particular,
we provide tests which work for noninvariant
measures if an invariant
measure equivalent to a natural measure exists but its density
function is not known. Examples of families of interval maps and
complex maps on
the Riemann sphere illustrate the results.


Acknowledgements
This work was partly funded by the LMS (Scheme 2 grant 2603) and by EPSRC (grant GR/S91147/01)


Author information
Henk Bruin:
Department of Mathematics, University of Surrey, Guildford Surrey, GU2 7XH United Kingdom
h.bruin@surrey.ac.uk
Jane Hawkins:
Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Chapel Hill, North Carolina 275993250
jmh@math.unc.edu

