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On the equivalent classification of three-dimensional competitive Atkinson/Allen models relative to the boundary fixed points
Holonomies and cohomology for cocycles over partially hyperbolic diffeomorphisms
1. | Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States |
References:
[1] |
A. Avila, J. Santamaria and M. Viana, Holonomy invariance: Rough regularity and applications to Lyapunov exponents, Asterisque, 358 (2013), 13-74. |
[2] |
K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems, Ann. of Math., 171 (2010), 451-489.
doi: 10.4007/annals.2010.171.451. |
[3] |
D. Dolgopyat, Livsic theory for compact group extensions of hyperbolic systems, Mosc. Math. J., 5 (2005), 55-67. |
[4] |
A. Katok and A. Kononenko, Cocycle stability for partially hyperbolic systems, Math. Res. Letters, 3 (1996), 191-210.
doi: 10.4310/MRL.1996.v3.n2.a6. |
[5] |
A. Katok and V. Nitică, Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem, Cambridge University Press, Cambridge, 2011.
doi: 10.1017/CBO9780511803550. |
[6] |
B. Kalinin and V. Sadovskaya, Cocycles with one exponent over partially hyperbolic systems, Geom. Dedicata, 167 (2013), 167-188.
doi: 10.1007/s10711-012-9808-z. |
[7] |
R. de la Llave and A. Windsor, Livšic theorem for non-commutative groups including groups of diffeomorphisms, and invariant geometric structures, Ergodic Theory Dynam. Systems, 30 (2010), 1055-1100.
doi: 10.1017/S014338570900039X. |
[8] |
R. de la Llave, Smooth conjugacy and SRB measures for uniformly and nonuniformly hyperbolic systems, Comm. Math. Phys., 150 (1992), 289-320.
doi: 10.1007/BF02096662. |
[9] |
M. Nicol and M. Pollicott, Measurable cocycle rigidity for some non-compact groups, Bull. London Math. Soc., 31 (1999), 592-600.
doi: 10.1112/S0024609399005937. |
[10] |
V. Nitică and A. Török, Regularity of the transfer map for cohomologous cocycles, Ergodic Theory Dynam. Systems, 18 (1998), 1187-1209.
doi: 10.1017/S0143385798117480. |
[11] |
Ya. Pesin, Lectures on Partial Hyperbolicity and Stable Ergodicity, European Mathematical Society (EMS), Zurich, 2004.
doi: 10.4171/003. |
[12] |
M. Pollicott and C. P. Walkden, Livšic theorems for connected Lie groups, Trans. Amer. Math. Soc., 353 (2001), 2879-2895.
doi: 10.1090/S0002-9947-01-02708-8. |
[13] |
V. Sadovskaya, Cohomology of fiber bunched cocycles over hyperbolic systems, Ergodic Theory Dynam. Systems, Available on CJO 2014.
doi: 10.1017/etds.2014.43. |
[14] |
K. Schmidt, Remarks on Livšic' theory for non-Abelian cocycles, Ergodic Theory Dynam. Systems, 19 (1999), 703-721.
doi: 10.1017/S0143385799146790. |
[15] |
M. Viana, Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents, Ann. of Math., 167 (2008), 643-680.
doi: 10.4007/annals.2008.167.643. |
[16] |
A. Wilkinson, The cohomological equation for partially hyperbolic diffeomorphisms, Asterisque, 358 (2013), 75-165. |
show all references
References:
[1] |
A. Avila, J. Santamaria and M. Viana, Holonomy invariance: Rough regularity and applications to Lyapunov exponents, Asterisque, 358 (2013), 13-74. |
[2] |
K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems, Ann. of Math., 171 (2010), 451-489.
doi: 10.4007/annals.2010.171.451. |
[3] |
D. Dolgopyat, Livsic theory for compact group extensions of hyperbolic systems, Mosc. Math. J., 5 (2005), 55-67. |
[4] |
A. Katok and A. Kononenko, Cocycle stability for partially hyperbolic systems, Math. Res. Letters, 3 (1996), 191-210.
doi: 10.4310/MRL.1996.v3.n2.a6. |
[5] |
A. Katok and V. Nitică, Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem, Cambridge University Press, Cambridge, 2011.
doi: 10.1017/CBO9780511803550. |
[6] |
B. Kalinin and V. Sadovskaya, Cocycles with one exponent over partially hyperbolic systems, Geom. Dedicata, 167 (2013), 167-188.
doi: 10.1007/s10711-012-9808-z. |
[7] |
R. de la Llave and A. Windsor, Livšic theorem for non-commutative groups including groups of diffeomorphisms, and invariant geometric structures, Ergodic Theory Dynam. Systems, 30 (2010), 1055-1100.
doi: 10.1017/S014338570900039X. |
[8] |
R. de la Llave, Smooth conjugacy and SRB measures for uniformly and nonuniformly hyperbolic systems, Comm. Math. Phys., 150 (1992), 289-320.
doi: 10.1007/BF02096662. |
[9] |
M. Nicol and M. Pollicott, Measurable cocycle rigidity for some non-compact groups, Bull. London Math. Soc., 31 (1999), 592-600.
doi: 10.1112/S0024609399005937. |
[10] |
V. Nitică and A. Török, Regularity of the transfer map for cohomologous cocycles, Ergodic Theory Dynam. Systems, 18 (1998), 1187-1209.
doi: 10.1017/S0143385798117480. |
[11] |
Ya. Pesin, Lectures on Partial Hyperbolicity and Stable Ergodicity, European Mathematical Society (EMS), Zurich, 2004.
doi: 10.4171/003. |
[12] |
M. Pollicott and C. P. Walkden, Livšic theorems for connected Lie groups, Trans. Amer. Math. Soc., 353 (2001), 2879-2895.
doi: 10.1090/S0002-9947-01-02708-8. |
[13] |
V. Sadovskaya, Cohomology of fiber bunched cocycles over hyperbolic systems, Ergodic Theory Dynam. Systems, Available on CJO 2014.
doi: 10.1017/etds.2014.43. |
[14] |
K. Schmidt, Remarks on Livšic' theory for non-Abelian cocycles, Ergodic Theory Dynam. Systems, 19 (1999), 703-721.
doi: 10.1017/S0143385799146790. |
[15] |
M. Viana, Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents, Ann. of Math., 167 (2008), 643-680.
doi: 10.4007/annals.2008.167.643. |
[16] |
A. Wilkinson, The cohomological equation for partially hyperbolic diffeomorphisms, Asterisque, 358 (2013), 75-165. |
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