Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higherrank abelian groups
Pages: 487  515,
Issue 3,
July
2010
doi:10.3934/jmd.2010.4.487 Abstract
References
Full text (331.2K)
Related Articles
Anatole Katok  Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)
Federico Rodriguez Hertz  IMERLFacultad de Ingeniería, Universidad de la República, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo, Uruguay (email)
1 
L. Barreira and Y. Pesin, "Lyapunov Exponents and Smooth Ergodic Theory," University Lecture Series, 23, AMS, Providence, R.I., 2002. 

2 
L. Barreira and Y. Pesin, "Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents," Encyclopedia of Mathematics and Its Applications, 115, Cambridge University Press, 2007. 

3 
D. Damjanovic and A. Katok, Local Rigidity of Partially Hyperbolic Actions. II. The geometric method and restrictions of Weyl chamber flows on $SL(n, R)$/$\Gamma$, www.math.psu.edu/katok_a/papers.html. 

4 
R. de la Llave, Smooth conjugacy and SRB measures for uniformly and nonuniformly hyperbolic systems, Comm. Math. Phys., 150 (1992), 289320. 

5 
M. Einsiedler and E. Lindenstrauss, Rigidity properties of $\mathbbZ^d$actions on tori and solenoids, Electron. Res. Announc. Amer. Math. Soc., 9 (2003), 99110. 

6 
H. Hu, Some ergodic properties of commuting diffeomorphisms, Ergodic Theory Dynam. Systems, 13 (1993), 73100. 

7 
B. Kalinin and A. Katok, Invariant measures for actions of higherrank abelian groups, Proc. Symp. Pure Math, 69 (2001), 593637. 

8 
B. Kalinin and A. Katok, Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori, Journal of Modern Dynamics, 1 (2007), 123146. 

9 
B. Kalinin, A. Katok and F. Rodriguez Hertz, New progress in nonuniform measure and cocycle rigidity, Electronic Research Announcements in Mathematical Sciences, 15 (2008), 7992. 

10 
B. Kalinin, A. Katok and F. Rodriguez Hertz, Nonuniform measure rigidity, Annals of Mathematics, to appear. 

11 
A. Katok, V. Nitica and A. Török, NonAbelian cohomology of abelian Anosov actions, Ergod. Th. & Dynam. Syst., 20 (2000), 259288. 

12 
A. Katok and V. Nitica, "Differentiable Rigidity of HigherRank Abelian Group Actions I. Introduction and Cocycle Problem," Cambridge University Press, to appear. 

13 
A. Katok and F. Rodriguez Hertz, Uniqueness of large invariant measures for $\Z^k$ actions with Cartan homotopy data, Journal of Modern Dynamics, 1 (2007), 287300. 

14 
A. Katok and R. J. Spatzier, First cohomology of Anosov actions of higherrank abelian groups and applications to rigidity, Publ. Math. IHES, 79 (1994), 131156. 

15 
A. Katok and R. J. Spatzier, Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions, Math. Res. Letters, 1 (1994), 193202. 

16 
F. Ledrappier and J.S. Xie, Vanishing transverse entropy in smooth ergodic theory, preprint. 

17 
F. Ledrappier and L.S. Young, The metric entropy of diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula, Annals of Mathematics, 122 (1985), 509539. 

18 
F. Ledrappier and L.S. Young, The metric entropy of diffeomorphisms. Part II: Relations between entropy, exponents and dimension, Annals of Mathematics, 122 (1985), 540574. 

19 
F. Rodriguez Hertz, M. Rodriguez Hertz, A. Tahzibi and R. Ures, A criterion for ergodicity of nonuniformly hyperbolic diffeomorphisms, Electronic Research Announcements in Mathematical Sciences, 14 (2007), 7481. 

Go to top
