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The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis
Measure and cocycle rigidity for certain nonuniformly hyperbolic actions of higher-rank abelian groups
1. | Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 |
2. | IMERL-Facultad de Ingeniería, Universidad de la República, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo, Uruguay |
References:
[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 $SL(n, R)$/$\Gamma$,, , ().
|
[4] |
R. de la Llave, Smooth conjugacy and SRB measures for uniformly and non-uniformly hyperbolic systems, Comm. Math. Phys., 150 (1992), 289-320.
doi: doi:10.1007/BF02096662. |
[5] |
M. Einsiedler and E. Lindenstrauss, Rigidity properties of $\mathbbZ^d$-actions on tori and solenoids, Electron. Res. Announc. Amer. Math. Soc., 9 (2003), 99-110.
doi: doi:10.1090/S1079-6762-03-00117-3. |
[6] |
H. Hu, Some ergodic properties of commuting diffeomorphisms, Ergodic Theory Dynam. Systems, 13 (1993), 73-100.
doi: doi:10.1017/S0143385700007215. |
[7] |
B. Kalinin and A. Katok, Invariant measures for actions of higher-rank abelian groups, Proc. Symp. Pure Math, 69 (2001), 593-637. |
[8] |
B. Kalinin and A. Katok, Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori, Journal of Modern Dynamics, 1 (2007), 123-146. |
[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), 79-92. |
[10] |
B. Kalinin, A. Katok and F. Rodriguez Hertz, Nonuniform measure rigidity,, Annals of Mathematics, ().
|
[11] |
A. Katok, V. Nitica and A. Török, Non-Abelian cohomology of abelian Anosov actions, Ergod. Th. & Dynam. Syst., 20 (2000), 259-288.
doi: doi:10.1017/S0143385700000122. |
[12] |
A. Katok and V. Nitica, "Differentiable Rigidity of Higher-Rank Abelian Group Actions I. Introduction and Cocycle Problem,", Cambridge University Press, ().
|
[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), 287-300. |
[14] |
A. Katok and R. J. Spatzier, First cohomology of Anosov actions of higher-rank abelian groups and applications to rigidity, Publ. Math. IHES, 79 (1994), 131-156.
doi: doi:10.1007/BF02698888. |
[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), 193-202. |
[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), 509-539.
doi: doi:10.2307/1971328. |
[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), 540-574.
doi: doi:10.2307/1971329. |
[19] |
F. Rodriguez Hertz, M. Rodriguez Hertz, A. Tahzibi and R. Ures, A criterion for ergodicity of non-uniformly hyperbolic diffeomorphisms, Electronic Research Announcements in Mathematical Sciences, 14 (2007), 74-81. |
show all references
References:
[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 $SL(n, R)$/$\Gamma$,, , ().
|
[4] |
R. de la Llave, Smooth conjugacy and SRB measures for uniformly and non-uniformly hyperbolic systems, Comm. Math. Phys., 150 (1992), 289-320.
doi: doi:10.1007/BF02096662. |
[5] |
M. Einsiedler and E. Lindenstrauss, Rigidity properties of $\mathbbZ^d$-actions on tori and solenoids, Electron. Res. Announc. Amer. Math. Soc., 9 (2003), 99-110.
doi: doi:10.1090/S1079-6762-03-00117-3. |
[6] |
H. Hu, Some ergodic properties of commuting diffeomorphisms, Ergodic Theory Dynam. Systems, 13 (1993), 73-100.
doi: doi:10.1017/S0143385700007215. |
[7] |
B. Kalinin and A. Katok, Invariant measures for actions of higher-rank abelian groups, Proc. Symp. Pure Math, 69 (2001), 593-637. |
[8] |
B. Kalinin and A. Katok, Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori, Journal of Modern Dynamics, 1 (2007), 123-146. |
[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), 79-92. |
[10] |
B. Kalinin, A. Katok and F. Rodriguez Hertz, Nonuniform measure rigidity,, Annals of Mathematics, ().
|
[11] |
A. Katok, V. Nitica and A. Török, Non-Abelian cohomology of abelian Anosov actions, Ergod. Th. & Dynam. Syst., 20 (2000), 259-288.
doi: doi:10.1017/S0143385700000122. |
[12] |
A. Katok and V. Nitica, "Differentiable Rigidity of Higher-Rank Abelian Group Actions I. Introduction and Cocycle Problem,", Cambridge University Press, ().
|
[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), 287-300. |
[14] |
A. Katok and R. J. Spatzier, First cohomology of Anosov actions of higher-rank abelian groups and applications to rigidity, Publ. Math. IHES, 79 (1994), 131-156.
doi: doi:10.1007/BF02698888. |
[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), 193-202. |
[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), 509-539.
doi: doi:10.2307/1971328. |
[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), 540-574.
doi: doi:10.2307/1971329. |
[19] |
F. Rodriguez Hertz, M. Rodriguez Hertz, A. Tahzibi and R. Ures, A criterion for ergodicity of non-uniformly hyperbolic diffeomorphisms, Electronic Research Announcements in Mathematical Sciences, 14 (2007), 74-81. |
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