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Local rigidity of homogeneous parabolic actions: I. A model case
1. | Department of Mathematics, Rice University, 6100 Main St., Houston, TX 77005, United States |
2. | Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 |
References:
[1] |
E. J. Benveniste, Rigidity of isometric lattice actions on compact Riemannian manifolds, Geom. Funct. Anal., 10 (2000), 516-542.
doi: 10.1007/PL00001627. |
[2] |
D. Damjanović, Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions, J. Mod. Dyn., 1 (2007), 665-688.
doi: 10.3934/jmd.2007.1.665. |
[3] |
D. Damjanović and A. Katok, Local rigidity of restrictions of Weyl chamber flows, C. R. Math. Acad. Sci. Paris, 344 (2007), 503-508. |
[4] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl chamber flows on $SL(n, R)$$/\Gamma$, Int. Math. Res. Notes, 2010.
doi: 10.1093/imrn/rnq252. |
[5] |
D. Damjanović and A. Katok, Local rigidity of actions of higher-rank abelian groups and KAM method, Electron. Res. Announc. Amer. Math. Soc., 10 (2004), 142-154. |
[6] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions I. KAM method and $\Z^k$ actions on the torus, Ann. of Math. (2), 172 (2010), 1805-1858. |
[7] |
D. Fisher, First cohomology and local rigidity of group actions,, Ann. of Math., ().
|
[8] |
L. Flaminio and G. Forni, Invariant distributions and time averages for horocycle flows, Duke Math. J., 119 (2003), 465-526. |
[9] |
R. S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.), 7 (1982), 65-222. |
[10] |
B. Hasselblatt and A. Katok, Principal structures, in "Handbook in Dynamical Systems," 1A, North-Holland, Amsterdam, (2002), 1-203. |
[11] |
A. Katok and R. Spatzier, Differential rigidity of Anosov actions of higher-rank abelian groups and algebraic lattice actions, Proc. Steklov Inst. Math., 216 (1997), 287-314. |
[12] |
D. Mieczkowski, The first cohomology of parabolic actions for some higher-rank abelian groups and representation theory, J. Mod. Dyn., 1 (2007), 61-92.
doi: 10.3934/jmd.2007.1.61. |
[13] |
D. Mieczkowski, "The Cohomological Equation and Representation Theory," Ph.D thesis, The Pennsylvania State University, 2006. |
[14] |
J. Moser, On commuting circle mappings and simoultaneous Diophantine approximations, Math. Z., 205 (1990), 105-121.
doi: 10.1007/BF02571227. |
[15] |
F. Ramirez, Cocycles over higher-rank abelian actions on quotients of semisimple Lie groups, J. Mod. Dyn., 3 (2009), 335-357.
doi: 10.3934/jmd.2009.3.335. |
[16] |
E. Zehnder, Generalized implicit-function theorems with applications to some small divisor problems. I, Comm. Pure Appl. Math., 28 (1975), 91-140. |
[17] |
Z. Wang, Local rigidity of partially hyperbolic actions, J. Mod. Dyn., 4 (2010), 271-327.
doi: 10.3934/jmd.2010.4.271. |
[18] |
Z. Wang, New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions, J. Mod. Dyn., 4 (2010), 585-608.
doi: 10.3934/jmd.2010.4.585. |
show all references
References:
[1] |
E. J. Benveniste, Rigidity of isometric lattice actions on compact Riemannian manifolds, Geom. Funct. Anal., 10 (2000), 516-542.
doi: 10.1007/PL00001627. |
[2] |
D. Damjanović, Central extensions of simple Lie groups and rigidity of some abelian partially hyperbolic algebraic actions, J. Mod. Dyn., 1 (2007), 665-688.
doi: 10.3934/jmd.2007.1.665. |
[3] |
D. Damjanović and A. Katok, Local rigidity of restrictions of Weyl chamber flows, C. R. Math. Acad. Sci. Paris, 344 (2007), 503-508. |
[4] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl chamber flows on $SL(n, R)$$/\Gamma$, Int. Math. Res. Notes, 2010.
doi: 10.1093/imrn/rnq252. |
[5] |
D. Damjanović and A. Katok, Local rigidity of actions of higher-rank abelian groups and KAM method, Electron. Res. Announc. Amer. Math. Soc., 10 (2004), 142-154. |
[6] |
D. Damjanović and A. Katok, Local rigidity of partially hyperbolic actions I. KAM method and $\Z^k$ actions on the torus, Ann. of Math. (2), 172 (2010), 1805-1858. |
[7] |
D. Fisher, First cohomology and local rigidity of group actions,, Ann. of Math., ().
|
[8] |
L. Flaminio and G. Forni, Invariant distributions and time averages for horocycle flows, Duke Math. J., 119 (2003), 465-526. |
[9] |
R. S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.), 7 (1982), 65-222. |
[10] |
B. Hasselblatt and A. Katok, Principal structures, in "Handbook in Dynamical Systems," 1A, North-Holland, Amsterdam, (2002), 1-203. |
[11] |
A. Katok and R. Spatzier, Differential rigidity of Anosov actions of higher-rank abelian groups and algebraic lattice actions, Proc. Steklov Inst. Math., 216 (1997), 287-314. |
[12] |
D. Mieczkowski, The first cohomology of parabolic actions for some higher-rank abelian groups and representation theory, J. Mod. Dyn., 1 (2007), 61-92.
doi: 10.3934/jmd.2007.1.61. |
[13] |
D. Mieczkowski, "The Cohomological Equation and Representation Theory," Ph.D thesis, The Pennsylvania State University, 2006. |
[14] |
J. Moser, On commuting circle mappings and simoultaneous Diophantine approximations, Math. Z., 205 (1990), 105-121.
doi: 10.1007/BF02571227. |
[15] |
F. Ramirez, Cocycles over higher-rank abelian actions on quotients of semisimple Lie groups, J. Mod. Dyn., 3 (2009), 335-357.
doi: 10.3934/jmd.2009.3.335. |
[16] |
E. Zehnder, Generalized implicit-function theorems with applications to some small divisor problems. I, Comm. Pure Appl. Math., 28 (1975), 91-140. |
[17] |
Z. Wang, Local rigidity of partially hyperbolic actions, J. Mod. Dyn., 4 (2010), 271-327.
doi: 10.3934/jmd.2010.4.271. |
[18] |
Z. Wang, New cases of differentiable rigidity for partially hyperbolic actions: Symplectic groups and resonance directions, J. Mod. Dyn., 4 (2010), 585-608.
doi: 10.3934/jmd.2010.4.585. |
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